0:02 Hi everybody. How is everyone? Buddy.
0:03 I really hope you guys clicked.
0:05 It must be there on this video that friend, there is such a
0:06 I can find a video, I can find a lecture like this,
0:08 I want to find a teacher who will
0:09 Clear trigonometry in one go.
0:11 Because from where I have studied till now
0:12 But I did not understand anything. And if you understand something
0:14 Trigonometric Identities
0:16 Questions are not being made. Difficult
0:18 I wonder what this chapter is about.
0:19 Theta? What is cos theta? understand something
0:22 It is not coming. Here. Today this lecture
0:24 I can promise you after I see it
0:26 Am. Trigonometry should be completely clear
0:28 Will go. Thick books like RD Sharma
0:30 He too has questions, you should answer them in this lecture.
0:32 Seeing this you will do it very easily
0:33 It is guaranteed. I'm not just saying this, I
0:35 I will show you. Of course, this lecture is a bit
0:38 It will be long because I am trying my best.
0:40 I mean all the questions from last year
0:41 Those are the maximum questions I have for you
0:44 Let me cover it in this video. NCERT
0:47 It's done, NCERT exemplar is done. of all
0:48 I will make all the questions very easy for you.
0:50 Should I give it? Ok? I just need you with me,
0:52 I need your patience. Ok? It is possible
0:55 This face is new for you but for me it is new
0:58 Treat everyone like an elder brother and trust them.
1:00 I will clear A to Z, start now
1:02 You will study from the very basics and it will be very interesting.
1:03 Read the method and if the video is long
1:05 It is not necessary to look at the parts part by part.
1:07 Who said boss, 3 hours video in one
1:09 I don't want to see you together, I feel like
1:10 First I watch for 1 hour, then I watch for 1 hour, then again for 1 hour
1:12 If I look at the clock, you look at it that way.
1:13 The important thing is to complete it
1:15 Because if you give this a lecture
1:17 After completing this, you will get your
1:20 You hardly need to do anything from the side. Ok?
1:21 So let's start with this
1:23 The Story of Trigonometry. Joe First Half
1:24 Off the video it's much easier.
1:26 You may have some in the next half.
1:27 Some difficulties may come but I am here, nothing will happen.
1:29 One. Let's start boss. Ok? Let go
1:32 So first of all, friend, the meaning of trigonometry
1:34 What is? Listen. Listen to me. Ok?
1:36 Trigonometry means right angle triangles
1:38 I am talking about. Trigonometry Meaning
1:40 I am talking about right angle triangle. Now
1:42 First of all, when a right angle triangle
1:44 Please pay attention when I talk. As if
1:46 I made a right angle triangle. Now if
1:48 Let me ask you guys, suppose I wrote this in A
1:50 I said it was B, I said it was C
1:53 spoke. Now if I ask you guys,
1:55 What is the hypotenuse in a right angle triangle?
1:58 Is? Hypotension means the side that is the longest
2:01 It is long. You guys should know
2:04 That boss, if it is 90° here then it is 90°
2:06 front, 90's front, 90's
2:10 The person in front is always your hypo.
2:13 Always the one in front of Always 90
2:15 Hypo. Is it clear? Now listen. Now if I
2:18 Let me ask you what is the base of this triangle?
2:21 will be? What would be perpendicular? So mostly
2:23 People might say that the base will be this,
2:26 This will be perpendicular. But don't say it like that
2:29 It is now. This is the most important and the first
2:32 What about trigonometry? that angle's
2:34 according to the reference angle, your
2:36 Base and perpendicular disc. My
2:39 What do you mean? For example, if I
2:42 Let me tell you, I took this angle.
2:43 If I tell you that I have
2:46 Took the angle of. Ok? So from this angle
2:48 What will be the base for this? For this angle
2:50 What would be perpendicular? listen to me
2:52 be careful. Now the base for this angle will be
2:55 The one just next to it. Or you think like this
2:57 Can you brother, with whom is this angle being formed?
2:59 Is? From this side, from this side, from this side,
3:01 From this side. So neither of these two
3:04 There must be some base. Now this one is hypo. So
3:06 The leftovers should be your base. This means to say
3:09 The other side becomes your base. and automatically
3:15 The person in front of him would not have been your perpendicular. Is.
3:17 Is.
3:19 clear? Ok? Now listen to the important thing.
3:23 Ok? Another name for base
3:26 Adjacent side. All the things just
3:28 keep listening. Keep watching things calmly.
3:30 Ok? We call it perpendicular
3:33 Opposite side. Because this angle is opposite
3:36 it occurs. Ok? Now let me ask you a question
3:38 I do. As if I made this triangle.
3:41 ok sir. As if I called it A. This
3:43 I said A, this I said B, this
3:46 I said c. This is your 90. If I you
3:48 I should tell people about the reference of this angle.
3:50 I am talking. Respect for this angle
3:52 I am talking. So for this angle
3:54 What will be the base? What would be perpendicular?
3:57 What would be hypotensive? Simple. in front of 90
4:00 Wala is always hypo. In front of Always 90
4:02 Always gonna hypo. Good. Now what is the base?
4:04 will be? This angle is formed by joining this side
4:06 It is being formed and is being formed from this side. in
4:08 It is being made from both sides. Now these
4:10 There will be some base on either side.
4:12 So this one is hypo so the one next to it is yours
4:16 It will be the base. Understand? and just in front of it
4:20 This is your perpendicular
4:23 It will happen. Ok? Perpendicular to your
4:26 also called the opposite side and the base is called its
4:29 Also called adjacent side. So understand one thing
4:31 Let's see how easy it is. So trigonometry
4:33 Meaning we are talking about a right angle triangle.
4:34 Is. You guys are another one in a right angle triangle.
4:37 What did you learn? that perpendicular, base and
4:41 It is decided according to the hypo angle.
4:43 Ok? Now the meaning of the word trigonometry
4:45 Do you understand? Break it down and understand it. Look at what
4:47 Trigonometry word is very easy, isn't it?
4:49 Easy. So the trigonometry word is those two
4:52 It is made up of words. Trigon End
4:55 Metron. Ok? Now the meaning of Trigonon
4:58 What is? Simple. It means triangle.
5:01 What does it mean? It means
5:03 Triangle. And what does it mean to be a matron?
5:06 Measurement takes place. What does metron mean?
5:09 This is measurement. Meaning of Measurement of Triangles
5:11 I am going to do it in this particular chapter
5:13 I. triangle measurer
5:16 I am in this particular chapter. Which ones
5:18 Of triangles? of a right angle triangle. Now
5:20 Right angle triangle major means three
5:22 You can measure the sides and three angles.
5:24 Can measure three sides and three angles
5:27 yes. So basically trigonometry is about
5:29 Measuring of Right Angle Triangles.
5:31 Measurement of Right Angle Triangles You can find it here
5:34 But let's do it. Trigonometry Means the Science
5:37 of Measuring Triangles. of trigonometry
5:39 Meaning The Science of Measuring Triangles. Now
5:41 How do they do this? You will need a lot for that
5:43 There is a need to learn important things. whose
5:45 The name is trigonometric ratios.
5:47 What is the name? Do you hear it? Its
5:49 It means trigonometric ratios.
5:52 Listen very carefully. Ok? Now it happened
5:54 What? What happened now? As if I had written
5:56 Angle triangle made. Everyone listen carefully
5:58 From. As if brother, I have taken a right angle
6:03 Triangle made P QR and here Q 90 say
6:06 Gave. Now, as if I have respected this angle
6:07 I talked. In respect of this angle.
6:09 Or let's do one thing. of this angle
6:12 Let's talk with respect. and this angle
6:15 I call this something theta. What does it mean
6:18 It is theta. Ok? It is the Greek alphabet.
6:21 There is no need to be afraid. theta as x
6:23 is, y happens, this is how theta happens
6:25 It happens. Simple. Ok? Now keep listening
6:27 Brother. Isn't it? Look, now you all know.
6:33 that for this this base, this hypo, this Perpendicular.
6:35 Perpendicular.
6:38 Is it clear? Now how many ratios should be made here?
6:40 Can I go? What do ratios mean? Two
6:43 Comparing things by division.
6:45 Ok? So now you can understand that brother or
6:49 So you take P/H means take both of them
6:51 Or take both of these or take both of these
6:53 Take. Apart from this, any ratio can be formed
6:56 What? Think about it, I will tell you if it can be done.
6:59 Listen carefully brother, first of all you P / H
7:01 You can take it. Took the ratio of these two.
7:05 Then you can take P/ or B/H. Correct
7:08 Is? Both of them, both of them. then these
7:10 Take both of them. Or you can take P/B
7:13 yes. Look, three ratios have come. Now you can use it
7:15 You can take it the other way around as well. You instead of P / H
7:20 Take H/P. Instead of H / P B / H you can use H / B
7:22 Take. Listen to what I'm saying
7:26 Then you will understand. Replace P/B with B/P
7:29 Take. What do I mean? you think so
7:31 That there are three people. What kind of friendship is theirs?
7:33 Can it be done in this way? Boss. either these two
7:36 can be friends. P / H Either or both
7:38 It could be either or both of these.
7:40 Did you understand? So there are three types of friendships.
7:43 Might be possible. But I did the opposite as well
7:45 Gave. Just think about this. So total
7:48 Six Trigonometric Functions in Trigonometry
7:51 There are ratios. Just six. Why six?
7:53 I explained that there could only be six. Correct
7:56 Is? These six ratios were given some names.
7:59 Like brother, now suppose there are five people in a family
8:01 If there are children, then the names of all five children will be given.
8:03 Will go. Isn't it? Now named in two ways
8:05 I go there often. The majority would have been like this
8:07 There is a long name and a short name
8:09 It happens that brother, suppose it is someone's name
8:11 Balraj. So why Billu, come here? So
8:14 Balraj his elder name Billu his nick name
8:17 short name. Isn't it? Likewise, this child
8:19 Name given. This ratio was named
8:23 sin theta. What? sin theta. Keep listening. All
8:24 You will understand. What am I saying? But
8:26 You will understand in the next 15 minutes. wait
8:29 Bus. Ok? We call this sin
8:32 Theta. How do you do Reed? sin of angle
8:36 theta sin of angle theta slowly understand everything
8:38 I will learn to be patient. Ok? name it
8:41 Given cosine
8:44 theta or cosin of angle theta. This
8:50 What name was given? Tangent of angle theta.
8:52 Ok? Or tangent theta. what to this
9:02 cosec of angle theta. Did you understand? This
9:04 Named Boss seconds
9:06 seconds
9:08 off angle theta. It was named
9:12 Cotangent of angle theta.
9:15 cotangent theta. Patience will make everything clear
9:17 Keep. Now these were becoming very big names.
9:19 So brother, I gave them short names. Such as
9:22 This is called sin theta in short form.
9:26 This is called cos theta in short form.
9:30 This is called tan theta in short form.
9:32 told this
9:34 cosec theta in short form. tell this
9:38 Given sec theta in short form. tell this
9:41 Given cot theta in short form. So total
9:44 There are four total six trigonometric ratios.
9:48 Are. Everyone will remember. sin theta, cos
9:50 theta, tan theta, cosec theta, sec theta,
9:53 cot theta. Are you able to understand this?
9:55 Are you able to understand this? So basically
9:57 What does it mean? If I tell you that
10:00 What is Boss sin theta? So perpendicular.
10:02 Hypo's ratio. Let me give you an example.
10:03 Then I will also teach you how to remember. Don't worry.
10:05 So for example, suppose I drew a triangle
10:07 Took. Everyone will listen carefully. Brother, believe
10:10 I took a triangle pqr. Ok? Now
10:12 Everyone listen carefully. Ok? Now believe
10:15 I called this angle theta. Ok? I
10:18 I am giving you this is your five. I
10:20 I am telling you that this is your five. These
10:22 You have four. This is your three. Ok? As such
10:24 Let's say right angle triangle, okay? Now if
10:27 I ask you guys to tell me the most
10:31 First tell me what will sin theta be? So
10:33 What is simple sin of angle theta?
10:36 Ratio of perpendicular and hypotenuse
10:39 Sir. So theta for theta for angle
10:41 perpendicular base and hypotenuse
10:44 It happens. So this one for theta
10:46 Everyone will pay attention to Theta. This one
10:50 This will be the base for theta. This perpendicular
10:53 will be. This will be hypo. So here comes your answer
10:57 Gaya Perpendicular how much four hypo how much
11:01 So the value of sin theta is 5.4/5.
11:03 Well, if I tell you guys that I
11:07 Tell me tan of angle theta then what is tan theta
11:09 then tan theta is perpendicular and
11:12 Base Ratios You Should Remember
11:14 at to theta to theta to theta
11:17 Base for perpendicular theta then theta
11:20 What is perpendicular to the boss?
11:22 what is base four and base three
11:24 4 / 3 This answer has come. How easy it is. If
11:27 Let me tell you what cot theta is.
11:29 will be? So you know the base
11:32 If it is perpendicular then what is the base? Three.
11:36 How perpendicular? Four. So it's 3/4.
11:38 Ok? Another question. comfortably at ease
11:40 Keep listening comfortably. Just keep listening. All
11:43 I will get it done. Have the confidence to not take tension
11:45 Of. Let's take ABC triangle. accept it
11:48 that at 90 now this time I'm going to focus on this angle
11:50 I am speaking of Theta. Ok? Suppose I
11:53 Let's call this angle theta or let's say x
11:56 I said it. Don't be afraid. x said it. Correct
11:58 Is? Now I respect this angle
12:00 I am talking. Ok? Now consider this
12:03 I said small a, I said this b
12:06 I asked him, what is the problem? Lyrics
12:09 Can I? Ok? So boss tell me
12:12 Everyone what is the value of sin x?
12:15 The value of sin x. sin of angle x means
12:19 What is? It means sin of
12:23 Angle x means it is easy so it is simple
12:26 sin x means the ratio of perpendicular hypo
12:28 But what is important is that x
12:30 according to this angle
12:33 Perpendicular base and hypode
12:36 So brother, perpendicular to this angle
12:39 What will become of this base, what will become of this
12:42 This will remain hypo, this is clear to everyone brother
12:44 The base for this angle is perpendicular to
12:47 Hypo just keep all the values. So
12:51 How perpendicular? Small b hypo how much?
12:54 How much hypo? A then b / a came. Let's go now
12:57 If I ask you what is the cos of angle x?
13:00 What will be the value or the value of cos x?
13:02 The value of cos x is simple. So cos x is
13:06 Is there a ratio? of the base and hypotenuse. So
13:08 angle with respect to x
13:10 What is the base according to this? base by x
13:14 is c and hypo is small a. So here it comes
13:18 Your c/a Easy-Pee Lemon Squeeze Clear
13:20 Is it true? Ok? Now brother, whenever the right
13:22 When it comes to angle triangle, a person
13:24 is always named. that person's
13:27 What is your name? Pythagoras. So brother, one
13:30 And everyone should understand that any
13:33 Any right angle in a right angle triangle
13:36 One thing is always valuable in a triangle.
13:40 Is. Pythagoras Theorem.
13:44 Pythagoras Theorem. You should know this
13:47 It will be useful. Ok? at your level
13:49 I will explain everything about how the questions will come. Tension
13:51 Don't take it. I have come with a lot of questions.
13:54 Lots of them. Every question is cleared here.
13:56 I will do it within this one video. Correct
13:58 Is? Everyone should know that the hypotheses
13:59 The square of the hypotenuse is
14:01 Perpendicular Square Plus Base Square
14:04 A right angle triangle is equal to
14:06 In. In a right angle triangle. So you
14:08 What to remember from here is that for example
14:11 Suppose you have a perpendicular triangle
14:14 If you have given the base, you can find the hypo
14:17 You can. As if perpendicular is given, hypo
14:20 If it is given then you can remove the base. As if a
14:22 If base and hypo are given then you are perpendicular
14:24 You can take it out. Let me ask you a question. One
14:25 Let's ask questions. As if I had made a right
14:28 Took angle triangle. Ok? Listen everyone
14:30 be careful. As if I told you that these seven
14:32 Is. And I told you that this is five.
14:36 Tell me what will it be? It's easy brother. You
14:39 Right now, consider anyone base perpendicular.
14:41 It's not going to make any difference. Let's assume I
14:44 If you take this angle, this is your base.
14:46 Will be done. This is your perpendicular, this is your
14:48 There is hypofix. So you should know that
14:50 What happened to Hypo's square?
14:52 Perpendicular square plus base square.
14:56 So brother, hypo square perpendicular
15:00 What? Square of five. What is the base? 7 of
15:01 Square. So the value of hypo square is
15:05 Have you arrived? square of 25 7 is 49
15:08 Hypox yours has come 49 + 25 so five here
15:13 When it went, it became 54 and 74. Ok? Now carefully
15:15 So what will be the value of hypotenuse? When
15:18 also square goes there plus minus
15:21 The square root of 74 becomes like this. whenever
15:23 Square will go there and two values will come out. One
15:26 Plus under 74 is a minus under 74.
15:29 But because the hypotenuse is the length of one side
15:32 Is. It will never be negative. So
15:35 74 Your answer will come. Now if you want it
15:38 You can simplify it a little bit like this: 74
15:42 It is written 2 * 3 1 left 2 * 7, do you understand?
15:45 But this is a prime number. So now you
15:47 This cannot be simplified. This is like this
15:51 He is going to stay. Ok? Now suppose if this
15:53 In the question I ask you if this
15:55 In the question I ask you that I
15:59 Tell me cosec of angle cosec, suppose I have
16:02 Theta said. So tell me cosec theta. So
16:05 What is the ratio of cosec theta? Hypotensive/Perpendicular.
16:08 Hypotensive/Perpendicular.
16:11 Now what is the hypo for this angle? this angle
16:13 Hypo is for
16:16 74 And what is perpendicular? Five. So this
16:20 You get the value of cosec theta. Understanding
16:21 Coming in? To be a little clearer
16:23 Brother, what's going on? What is
16:25 Trigonometric ratios? Ok? now one
16:29 Look at the method of remembering again. Correct
16:32 Is? Very easy, very easy, very easy. Correct
16:35 Is? perpendicular upon hypotenuse sin
16:38 Theta. base upon hypotenuse cos theta.
16:41 Perpendicular upon base tan theta. Hypotension
16:43 Upon perpendicular cosec theta. Hypotension
16:47 Upon base sec theta. Base / Perpendicular cot Theta.
16:49 Theta.
16:52 Easy, PG, lemon squeeze. Let us go. On this
16:54 based on this simple concept
16:56 Let's ask some questions. Trigonometric
16:58 I have told you the meaning of ratios. Correct
17:00 Is? Now let's start with some basics.
17:03 Let's ask questions. Ok? Now listen
17:05 Listen to me carefully. Now the first question you have
17:07 It comes down to the basics that you have a
17:09 Trigonometric ratio must be given. To you
17:11 To find all other trigonometric ratios
17:14 Will fall. As an example, for example
17:15 So let me ask you this question
17:18 I will show you. Ok? For example, you
17:20 Given cosec
17:24 of cosec of angle a cosec a cosec of angle
17:27 You've got the value of a cosec a is 10. To you
17:29 Said the remaining five trigonometric
17:32 Find the value of the ratios. from the same angle
17:34 for, for this angle, for this angle.
17:37 Do you understand? Ok? any angle
17:40 If you don't talk then you will have to go for angle A.
17:43 Have to take it out. Ok? How will you do it now? My
17:46 talk? Listen carefully. Ok? Look here. So,
17:50 cosec of angle A gave you 10. What
17:52 Can I rate this 10/1? any problem
17:54 No. Now cosec of angle A is
17:57 Is there a ratio, boss? Hypotension and
17:59 Keep listening to Perpendicular. Is this the thing
18:02 Are you getting it? Yes sir. Ok? Now
18:05 Because this is the ratio, we will not do this.
18:08 that the hypotenuse you took is 10 and
18:11 You took perpendicular to forest. This is wrong
18:14 Is. What do you have to do? something with it
18:16 You will have to put x. with it some x or else
18:20 Anything small a or k that you
18:24 You can do whatever you want. Let me put x.
18:27 Ok? What does it mean to say hypotensive you are 10
18:30 I will take 10x. Do not take the perpendicular one
18:33 Will take 1x. Now any trigonometric
18:34 What you need to know to calculate the ratio
18:37 Needed? The three sides of the triangle. Right
18:38 The three sides of an angle triangle.
18:40 Perpendicular, base and hypotenuse. Now
18:42 You know hypotenuse and perpendicular.
18:45 Take out the base. How easy it is. So boss, you
18:47 I know the formula. Square of hypo =
18:49 Perpendicular square plus base square.
18:51 Keep listening. So how much is a hypo? Easy.
18:54 Like hypo is the whole square of 10x
18:57 Perpendicular how much 1x the hole square base
19:01 I don't know how much, now pay attention, 10² 10
19:07 x² x² 1² 1 x² x² This is your base square.
19:11 Ok? Now 1x² comes here so 10x²
19:16 - 1x² = square of the base. So 10x² - 1x²
19:20 Focus on the square of the base. Correct
19:23 Is? Now we need the base value. So this
19:26 The square that comes here will be plus minus
19:29 It will be built and the entire thing will be under-routed.
19:32 This is your base value. Now base anytime
19:34 It cannot be negative. Listen to bass anytime
19:36 Brother, what does this mean? This means that the base
19:41 is coming to plus 9x²-- 9x². Now the base
19:43 It can never be negative. Brother, any
19:45 The length of a thing can never be negative.
19:47 So you will take this
19:51 of 9x² plus. Ok? Now what does this mean
19:52 Is? That
19:53 9 per separately
19:55 separately on x² because of the multiplication inside
19:58 It is written on it. Ok?
19:59 9 is 3
20:04 squared by the root of x² so 3x base is your size
20:08 Your base is gone 3x and your base is back 3x. Now hypotensive
20:10 I know, I know the perpendicular, I know the base.
20:12 Whatever trigonometric ratio you want
20:15 You can take it out. So first of all sin of angle
20:18 Let's take out A. Because angle A is
20:20 It is being curried. So what is the sin of angle A?
20:23 It happens? Perpendicular up hypotenus.
20:26 What is cos of angle? Base / Hypotension.
20:27 Hypotension.
20:30 What is tan of angle A? perpendicular
20:33 / Base. cosec is a given. cosec gave
20:36 It has happened. So
20:39 What is sec of angle A?
20:43 Hypotenuse / base and cotangent angle a
20:47 It happens? Base/Perpendicular. remember this
20:50 Needed Ok? Just keep all the things. Yours
20:53 The values will come. Ok? How much do you see? So
20:57 What is perpendicular? 1x Base What? 3x then 1x
21:02 Sorry hypotenus what? 10x. Ok?
21:06 10x. So look, x went to x. This is your 1/10
21:09 I have arrived. Whose value? Whose value? sin
21:12 The value of angle A. Ok? sin of angle
21:14 The value of A. Keep watching comfortably. Ok?
21:17 Now see how much base? Your base is 3X then base key
21:20 I wrote 3x instead. How much hypo? 10x then x
21:25 to x. This is your 3/10.
21:28 Correct? Do you understand? Ok? very easy
21:29 Is. It is very easy. what in time of angle
21:31 Done? Perpendicular. So brother
21:33 Perpendicular is 1x
21:38 The base is 3x x to the x. This is your 1/3
21:42 Went. Ok? What is sec of angle? sec
21:44 What is this off angle? Hypotension/Base. So
21:49 How much hypo? Hypo how much your 10x base?
21:55 Base your 3x x gone. Here you go, Route 10.
21:57 / 3
22:00 Ok? cot of angle is base /
22:03 Perpendicular. So what is the base? Base yours 3x
22:07 Perpendicular 1x x to x went here you have come
22:09 Three or 3/1, whichever you prefer.
22:11 Say it.
22:14 So the first basic question is whether a
22:16 The value of the trigonometric ratio will be given
22:19 The remaining five will have to be taken out. How
22:21 Want to remove it? Proper, I told you the method
22:23 Gave. Now a lot of kids here have this
22:26 I doubt whether it is necessary to put this x.
22:29 What? It has to be applied. It has to be applied. Without
22:32 Even if I tried, the answer would be the same. Putting the butt right
22:36 There is a way. Ok? Let's do this one.
22:38 Very simple question. just relax comfortably
22:40 Keep watching. What did you say? Brother. sin of
22:43 Angle A is given to you. Now you have a
22:44 The value of trigonometric ratio is given.
22:46 So you can calculate any trigonometric ratio.
22:48 You can extract the value. But what about you
22:51 spoke? Find the cos of A, find the tan of A,
22:53 Take out sec of A. Let's take it out. So,
22:57 What is the sin of angle A? 3/5 What would have happened
22:59 Is this it? perpendicular upon hypotenuse i.e.
23:02 Has the value of perpendicular come down to anything? 3x
23:04 And the value of hypo came to something like 5x, so now you
23:07 Remove the base. How will you remove it? hypotensive
23:09 Square Equal to Perpendicular Square
23:11 plus base square. So how much is a hypo?
23:15 How much is 5x² Perpendicular? of 3x
23:18 Square. How much is the base? Will have to remove it.
23:24 So 5² 25 x² x² 3² 9 x² x² is your base.
23:28 Square. So here you go, 25x²
23:32 - 9x² = Square of the base or your number
23:36 16x² = Square of the base here
23:40 So plus minus under root in the whole
23:43 ok it can't be negative
23:48 16x² = base square correct? So this is your
23:50 will go 16 separately
23:55 x² separately equal to base 16 is 4.
24:00 If this goes to x, then your base becomes 4x base.
24:03 Yours is 4x simple. Now that the base is here
24:05 You can calculate any trigonometric ratio.
24:08 You can. What is cos of angle a? Base
24:11 / Hypotension so what's the base come to? The base has arrived
24:17 4x hypo arrived 5x x to x went 4/5 arrived
24:20 The value of cos of angle a. Now I asked you
24:23 What is tan of angle a? So this is what happens
24:26 Perpendicular upon base. How perpendicular?
24:28 Perpendicular brother. Hey Perpendicular
24:32 Where did you go? Yes. So perpendicularly your 3x
24:38 Is. Base is your 4x. went from x to x. This is yours
24:42 3/4 has arrived. and asked you sec of angle a
24:45 So sec of angle a is the ratio of
24:50 Is? of the hypotenuse and base. Hypo Hai 5x Base
24:55 is 4x gone to x. Here you go 5/4
24:58 Easy. Too easy in my opinion. Now!
25:01 Till now, I think all the things are very easy.
25:03 She must be looking like this. Some more good level questions
25:06 I will get it done on this. Don't take tension. At once
25:08 I will get everything done. Ok? This is from NCERT
25:10 That is the question. Okay, right? Let's go in a triangle
25:13 ABC right angle at C so clearly given to you
25:16 what has happened is that tru brother look at the question
25:18 Do as much as you understand after seeing it.
25:20 I have to do it. Ok? so right angle at C so
25:23 The triangle is ABC.
25:26 Triangle ABC is right angled at C, so take
25:30 I take it. Right angle at C okay? from you
25:34 Say the value of tan of angle A is given as 1/3
25:36 Meaning, in respect of this angle, this angle
25:38 We are talking with respect. of this angle
25:40 We are talking with respect. Ok? So
25:42 If we are talking about this angle
25:44 then what is perpendicular base and hypo
25:47 will be? The one in front of 90 is always hypo
25:50 the base next to it the one in front of it Perpendicular.
25:52 Perpendicular.
25:55 Is it so clear? Now you have been given
25:59 If the value of tan of angle A is 1/3 then
26:01 You can do it yourself if a
26:02 The value of trigonometric ratio is given by
26:04 So you can know all the other trigonometric ratios.
26:06 You can find the value of . Let's take it out.
26:08 So it is simple. So brother, it is tan of angle
26:13 1/3 means this is your perpendicular upon base
26:16 Perpendicular is 1x
26:20 The base is take out 3x hypo. So hypo's
26:22 Square = Perpendicular Square + Base
26:26 Square so hypox perpendicular your 1x
26:30 Square base of 3x your square rest
26:36 So comfortably 1² 1 x² x² 3² 9 x² x² so this
26:40 There you have it: 1x² + 9x² 10x² hypo
26:42 square so the value of hypo is plus Minus
26:43 Minus 10x²
26:45 10x²
26:47 So your hypo is negative, right?
26:51 Can. So 10 10
26:56 x² x so 10x your hypo has arrived 10x
26:58 Your hypo.
27:01 Ok? Easy, come on, now you can do anything
27:03 Find the value of trigonometric ratio
27:05 You can. Okay, but what did he say to you? Attention
27:10 Give. Find the value of sin a * cos b +
27:15 cos a * sin b comfortably. I told you that sin
27:18 Find a * cos b + cos a * sin b. Rest
27:21 hear from. Now if I first calculate sin a
27:23 Should I talk? Everyone listen carefully. Ok?
27:25 If I talk about the sin of angle a
27:28 Everyone knows that this is perpendicular upon
27:30 Hypotension occurs. What should I do? I
27:32 its its its its values are different
27:35 I will take it out. But listen to me carefully.
27:37 Ok? The sin of angle A is
27:40 Perpendicular upon hypotenuse.
27:44 Ok? Now everyone pay attention, focus.
27:47 This is a little important. Now if I
27:50 Talking about angle a, for angle a
27:54 Perpendicular is 1x. The base is 3x. So angle a
27:59 The angle for is perpendicular to a is 1x.
28:04 The base is 3x and the hypo is yours
28:07 10x is for angle a. angle for angle a
28:09 For a. Ok? Now remove it so that
28:13 Don't be confused. Ok? Now focus.
28:16 Ok? sin of angle A perpendicular up
28:19 Hypotension. So for angle A
28:22 What is perpendicular to it? Write this here
28:29 Two 1X hypos what? root 10X so this is your 1/
28:32 10 has arrived. Ok? Now I told you cos of
28:35 angle B cos of angle B which is what?
28:39 Base/Hypo. Now listen comfortably. Now
28:42 Base for angle B, hypo for angle B.
28:45 So imagine angle B for angle B
28:47 What will be the base for angle A B? These
28:50 This is the base for angle B. Hypo then
28:53 There will be no change. 10 X so this is also your 1 /
28:56 10 has arrived. Just don't make a mistake. Angle's
28:59 Base and perpendicular will be decided accordingly.
29:03 Now we are talking about cos of angle a. This too
29:06 It will happen brother, base up hypo, but this time
29:09 What will be the base for angle a? So angle a
29:14 The base for this would be 3x hypo your 10x so x x
29:19 Here you go, you got your 3/10. Now sin b
29:22 There is talk going on. sin of angle b first sin of
29:24 We were talking about angle A. Now sin of angle
29:27 We are talking about B. Ok? Then angle B For
29:29 For
29:31 perpendicular to angle B then angle B
29:35 For angle B perpendicular to the given point, the angle will be 3X and
29:38 Hypo does not change. So this also comes
29:41 Yours is 3/10
29:45 Ok? Now look carefully. sin of angle A
29:48 The value of 1/10. sin of angle B
29:52 The value is 3/10 because here for angle A
29:55 Perpendicular hypo. Here, angle B
29:57 There is perpendicular hypo for. Angle's
30:00 Perpendicular base and hypotenuse
30:02 It is decided. This is the most important thing
30:06 Is. Now I told you sin A * cos B
30:13 sin A * cos B + cos A * sin B + cos A *
30:16 What is the value of sin B? So it is simple. sin a
30:20 What was the value coming out to be? 1/10 of cos b
30:23 What was the value coming in? Its also 1/10
30:26 What was the value of plus cos a? 3 /
30:31 Notice 3/10 of 10 sin b. So 1 * 1
30:39 1 10 * 10 10 so top 1 bottom 10 + 3 * 3 9
30:45 10 * 10 10 so brother below is 10 above is 1 + 9
30:51 So this 10/10 means the answer is one. Easy?
30:53 Easy?
30:55 This type of question will teach you trigonometric
30:58 Ratios can be asked. Very easy
31:02 The question is. This is a very simple question. Ok? Hi
31:03 Sorry to disturb. I came to tell you that
31:05 Like every time, this guy is here
31:08 I have come to save your tuition fees. Now
31:11 A very nice question friend NCERT
31:13 means this question you can expect
31:15 Maybe it could come in this way. Ok? Now
31:16 Look carefully here. After that I
31:19 Let me tell you some more basic things.
31:21 Yes, I have skipped it now. Ok?
31:23 In triangle PQR very easily
31:26 Reading the question. in triangle PQR
31:29 Right angle at Q is in triangle PQR
31:31 Right angle at Q, I can understand something.
31:35 It is proved that PQR is a triangle. The right angle is Q
31:39 But. Ok? Ok. Ok. Ok. PR
31:42 Well, one thing is clear to everyone. If you like this
31:45 If we know all three sides of the triangle
31:47 You can calculate any trigonometric ratio.
31:49 You can. This is what everyone understands
31:52 Brother. If you get this triangle
31:54 I will give it to you, I will give it to you, I will give it to you, all three sides
31:55 If I give it, then any trigonometry ratio
31:57 He will take it out. If I ask you guys
32:00 Tell me the sin of angle R. Will you tell me? Fear
32:02 Won't you be afraid, brother? Meaning of sin of angle R
32:04 I am talking in respect of this angle.
32:06 sin of angle P means respect to this angle
32:08 I am talking. You will tell me everything.
32:12 Ok? Now you were told that PR + QR rest
32:16 Read from. PR + QR equals 25. Good
32:22 PR + QR means this + this this + this look good
32:25 Let's see what this means? So PR
32:29 + QR is equal to 25. and PQ five good
32:32 PQ gave you a direct five. Ok?
32:34 So PQ gave you five. Listen comfortably.
32:36 First I am trying to understand the question.
32:38 Am. Ok? Determine the values of sin
32:42 P, cos P, tan P. You get the sin of angle P
32:44 Asked to find out, find cos of angle P
32:46 Told him to find the tan of angle P.
32:49 Meaning something in respect of this angle
32:51 Ask to find the trigonometric ratio
32:53 Are. One thing should come to everyone's mind that
32:55 If I need to know any trigonometric ratio
33:05 Should know. Yes or no? Yes sir.
33:06 So I do my main work. I this
33:08 I will find out both things. Because I have this
33:12 So I know. Now think about it and tell me
33:15 To find the value of two things i.e.
33:19 that the values of PR and QR PR and QR PR and QR
33:21 How many equations do you need to find out?
33:24 would need? If you have to compare two unknown things
33:27 If you want to find the value in maths then you have
33:29 There should be two equations. Is this clear?
33:31 There should be two equations. Those two equations
33:35 Where will they come from? There is an equation between these two
33:38 In the form of. One of these two forms
33:41 There is an equation. Where will the second one come from? Some?
33:43 Do you remember seeing the right angle triangle?
33:46 Pythagoras Theorem. So put that on. So
33:48 What does the Pythagorean theorem say? that its
33:50 Square its square plus its
33:52 will be equal to the square. So you understand
33:54 It should be understood that PR² PR²
33:56 PR²
34:02 will be equal to PQ² + QR². now you see
34:05 What happened? An equation in the form PR QR,
34:08 The second equation is in the form PR QR. in
34:12 Using both equations you can find PR QR PR QR
34:15 You will find out the value of. Now you will take it out
34:16 How? Look carefully. Ok? Just look
34:20 be careful. Ok? So this is your PR² PQ to you
34:24 I know five. So instead of this, five, so 5² 25
34:28 This is your QR². What do we do now? pay attention,
34:32 To focus. Pay attention, focus. Correct
34:35 Is? pay attention. Ok? This is an equation
34:38 Is. This is the second equation. Always remember this. If
34:41 One equation is linear. Linear means here
34:43 But whatever brother, suppose this is x, this is y then x
34:46 1 to the power of y, 1 to the power of y. If this is x then this
34:49 If x² then y² then y² is a linear equation
34:52 is a quadratic equation, so always
34:54 You have to make substitutions.
34:56 Substitution means changing the value of a variable
34:59 Take it out and throw it into another one. brother a variable
35:01 take the value from here and put it in the other
35:04 Two. What do you mean? pay attention. So
35:06 For example, if I picked it up here
35:10 As if I figured out the value of PR? 25
35:13 - QR will appear. Brother, the value of PR is QR there.
35:17 So 25-QR, did you understand this? You keep it here
35:21 Two. How? So instead of PR, PR becomes 25 - QR
35:23 So I am using this. pay attention. So
35:29 25 instead of PR - QR Instead of PR 25 - QR PR
35:33 Instead of 25 - QR and its square, this is yours
35:36 25 + QR²
35:38 I'll tell you once again what I did
35:40 This is a linear equation from here, any
35:43 Find out the value of the item. Suppose I did PR
35:46 If we calculate 25 - QR then we get it from the second equation
35:50 Throw it in. Ok? So now what is a - b²?
35:52 It happens? its square brother the square of a
36:00 So this is your 25 squared plus qr² - 2
36:06 a b = 25 + qr² Note
36:08 What to do? If the values of both of these
36:10 If I take it out, I will do any trigonometry
36:16 I can calculate the ratio. Now 25² 625 qr²
36:20 qr² 2 * 25 50qr
36:26 = 25 + qr² Now look at one thing. these qr² when is
36:29 If we go to the other side of the equal to sign then the minus sign
36:32 will become qr². So qr² over here plus this over there
36:36 going to minus qr² then plus qr² plus
36:39 will be cut off by qr². is plus of qr² plus of
36:42 How to cut it off from qr²? Understand the matter. If
36:47 If this + qr² goes there then it will become minus qr²
36:50 No. So + qr² - qr² will be cut off. I
36:52 Cut it directly. Ok? now here
36:56 What's left? Now your balance here is 25 625.
36:58 Get a job done 625
37:02 -How 25? Take it over there. So brother, this
37:05 Your plus will become 50 qr. It is easy. Now
37:10 See how the QR came out? 625 - 25 = 600 50QR
37:13 50QR
37:16 = 50 QR in 50 multiplication with QR
37:20 So if it comes here and gets divided then how will the QR
37:23 50 went down to zero went to zero 5 12 60
37:27 So look, your QR has arrived. Your 12 QRs have arrived.
37:30 12 and QR came 12 so PR just left
37:34 How brother? Substitute this QR into any one equation
37:37 Drop the value of. I would throw it in this
37:41 Am. So see how much PR you will get? PR
37:44 equals 25
37:48 - How much is QR? 12 So your PR has arrived
37:54 13. PR 13. Now think and see for yourself that your QR code will come.
37:58 12 went, PR came 13. Right Angle Triangle
37:59 All three sides came. You are anyone
38:02 You can calculate trigonometric ratios.
38:04 Very easy. Come, let me take it out. so sin of
38:06 To find angle P, sin of angle P
38:09 how much is a? Perpendicular upon hypo.
38:12 for angle P for angle P
38:14 perpendicular to the
38:18 This will be hypo. This is 12/13. cos
38:22 What is off angle P? Base/Hypo. So
38:24 for angle P for angle P
38:27 What for? The base will be five. Hypothera. Memory
38:30 Place the perpendicular base according to the angle and
38:33 Hypoticide occurs. What else did he say? tan
38:36 of angle P is tan of angle P
38:39 Perpendicular upon base. angle for angle P
38:43 Angle about P perpendicular to P
38:47 12 base five. So it came to 12/5. So an answer
38:50 This, this is an answer, this is an answer. NCERT's
38:54 A very beautiful question. Exercise 8.1
38:57 This is a question of this. Ok? Easy. Ok?
38:59 Now let's talk about something a little more basic.
39:01 What you should understand, you should know
39:04 Should be. Ok? Again Let's Let's Go
39:07 Down to the basics. Listen carefully. Correct
39:12 Is? Now when I write sin of angle
39:16 A. Well, I wrote it like this. It means
39:20 sin of angle A. Everyone is understanding this.
39:22 I will shorten this to sin A, sin A,
39:24 Do sin A, sin A, sin a. Well, its
39:26 What is long form? Its long form is sin
39:27 sin
39:31 No, one e comes. Ok? Is it clear? Now
39:33 For example, if I am talking to you people
39:36 I mean cos of angle a so whose short is this
39:39 Is there a form? This is the short form of cosin of
39:42 of angle A. Remember or not? cosine of angle A
39:44 Of. I have called it cos A in short form.
39:45 Gave. I have shortened it to cos A.
39:49 I said it. Ok? How will Reed do it? cos
39:53 of angle A cos of angle A. now over here
39:55 What mistakes children make is not your fault.
39:58 Brother, what does it mean for example
40:01 If the value is sin a, it does not mean that
40:06 That sin * angle a sin * angle a is wrong.
40:10 This is wrong. Understand? Meaning of sin of angle A
40:14 It is not that sin * angle A, this does not happen automatically.
40:17 There is one useless thing in it. This in itself is a
40:19 This is nonsense. Any trigonometric
40:22 Ratio moves with angle. with angle
40:25 It works. I mean, don't think that brother.
40:28 As if it is written somewhere tan theta. So its
40:33 would mean tan * theta. This is wrong. This is wrong
40:38 Is. Ok? Did you understand? Easy. Ok? Now
40:41 Come and talk about the basics. Let me tell you if I'm nice to you
40:43 People tell me any right angle triangle
40:45 Which is the largest side? Any
40:47 Also the largest side of a right angle triangle
40:49 He is hypotensive. Meaning of hypotensive
40:52 There cannot be a side larger than this. meant to say
40:55 The hypotenuse will be more than perpendicular
40:58 Will be big. The hypotenuse will be greater than the base
41:01 It will also be bigger. Did you understand? This is clear
41:04 talk? It is clear to everyone that the
41:07 The hypotenuse is the right angle triangle
41:09 The largest side is larger than the other two sides.
41:12 Must be. This is clear. So if I give you
41:14 Let me ask you a question, listen if I ask you a question
41:18 Should I say, brother, consider it as sin of angle
41:20 B in a question or let's sin off
41:24 Angle theta is given in a question
41:28 7 / 3 Is this possible? Is this so
41:30 Is it possible? Think about it. Think about it. Thinking
41:33 Look at this. Think about it. The value of sinθ is 7 /
41:35 3 Can this happen? you guys will say
41:39 Well, that's what this is, perpendicular hypo.
41:42 Perpendicular 7x Hypo 3x Base will come out.
41:44 All three sides of a right angle triangle are
41:46 Will go. But this is not to be done like this. I've just
41:50 This has been asked. Is the value of sin theta equal to 7/
41:52 3 is possible. What would you do? Look at this
41:55 Perpendicular/hypo occurs. Now you yourself
41:58 Think about it. Some 3x the value of hypo
42:00 Perpendicular value 7x
42:03 Hypo key value 3x, perpendicular key
42:06 Value 7x means you can see clearly
42:12 that hypo is smaller than perpendicular. Hypo
42:15 Smaller than perpendicular. You understand
42:16 What am I saying? Brother, here you are
42:18 Looks like hypo is something three.
42:22 Perpendicular is something seven times. Its
42:24 Meaning the perpendicular hypo became larger than the
42:28 That is not possible. Which is not possible.
42:32 Never greater than perpendicular hypo
42:34 will be. Always larger than hypoperpendicular
42:37 will be. The hypo will be greater than the base. So if you
42:39 If someone says the value of sin theta is 7 / 3 then this
42:41 Falls are not possible.
42:44 Some questions in NCERT based on this
42:46 are given. Look carefully. What are you saying
42:48 Are? State weather the following are true and
42:50 Falls. Justify your answer. We justify it
42:53 I will do it. So the value of sec a is 12 / 5
42:57 For some value of angle A. It just means that
43:01 that the sec of angle A can be 12 / 5
43:05 Is? Let's check. So sec of angle A
43:08 Gave 12/5. means sec of angle A what
43:12 It happens? Hypotension is up base. Hypo
43:16 some 12 base some five mean hypo some 12 *
43:19 x base something greater than 5 * x what hypo base
43:22 will be? Yes, this is possible. The answer has come
43:26 True. Ok? Let's look at the seconds. So cos
43:30 a cos a is the abbreviation
43:35 Used for cosec of angle a. cosec of angle
43:38 A cosec of angle A
43:43 cosc note cosc of angle a short of
43:45 What is a form? cos of angle a
43:50 The short form is cosec a or cos a
43:52 It happens? No cos a belongs to whom?
43:56 of the cosine. Short of cosine of angle A
43:58 has the form cos A. But in the question
44:00 What are you saying? He is saying this in the question
44:02 The short form of cosec of angle A is cos
44:06 A happens. Wrong wrong wrong wrong wrong. cosec off
44:08 The short form of angle a is cos a
44:11 cosec a is the short form of cosec of angle a
44:14 cosec a cosec of angle a is short
44:16 has the form cosec a cosec of angle a
44:19 If the short form is not cos a then brother
44:23 Sir, this is also a lie given to you.
44:27 Ok? What is the third one saying? cot a
44:31 is the cot a is the cosine product of cot
44:38 A. Well cot A is the remove this.
44:41 Okay, right? cot a is the product of cot A.
44:44 Does cot A mean this? cot A
44:49 Meaning cot * A. What cot A means
44:52 cot * A? No. I just taught you.
44:55 cot angle A, it's all the same thing. This
44:58 Don't break it and say cot into A.
45:01 This is wrong. Meaning this is a false statement.
45:04 cot A is not the product of cot and A.
45:07 Ok? What is the value of sinθ? could be 4/3
45:12 Is? Just look. The value of sinθ
45:15 sinθ Pay attention.
45:20 So brother, what should be the value of sinθ, 4/3
45:21 Can? Let's see. What is sin theta?
45:24 Perpendicular upon hypotenuse. perpendicular
45:27 Four, hypotenuse three. what perpendicular
45:32 Can be bigger than hypo? No. So falls.
45:35 Ok? Understand? This is your basic basic
45:38 There are things. Ok? Let's move on now
45:40 First. Ok? Now your next topic
45:42 It starts. We completed one thing
45:45 There are three things in total in Lee Chapter.
45:47 The first thing is trigonometric ratios which
45:49 I got you covered. Now the number two thing
45:51 Trigonometric ratios for some
45:53 Specific angles. Trigonometric
45:56 Ratios for some specific angles. But he
45:58 There is one important thing you need to learn
46:02 Needed Let me tell you what. Ok? See
46:04 if you notice if you notice okay
46:08 Everybody listen brother
46:12 What is this called reciprocal identity?
46:16 They talk about reciprocal identity a lot.
46:19 It's important to pay attention to your basics
46:22 I'm building it, okay, look, reciprocal.
46:25 Understanding what identity means
46:29 sin theta in the reciprocal identity
46:32 cosec commutes with theta. what is this
46:33 Are you speaking? I can't understand anything. Hey wait
46:39 Go, have patience for 2 minutes. Ok? cos theta
46:42 runs with sec theta. wait wait wait
46:44 I am telling you what it is?
46:48 tan theta commutes with cot theta. Are?
46:51 Guruji, did you not understand anything? I am telling you.
46:54 Brother, what is sin theta? sin theta subscript
46:56 I know, perpendicular.
46:59 I will do it with yellow. Everybody knows sin theta
47:02 It is perpendicular/hypo. correct
47:06 Is? What is cosec theta? Hypotension/
47:09 Are perpendicular. I don't understand anything that
47:11 What do you want to say? Now you will understand
47:14 In. Now you will understand why you are waiting. Correct Is?
47:16 Is?
47:19 When I'm saying sin theta, cosec
47:21 Theta are reciprocal of each other.
47:25 This means that if the value of sin theta
47:29 If you are getting 1/2 in any question then answer that question.
47:31 The value of cosec theta in the question is 2 / 1
47:36 Will come. If the value of sin theta is 7/12
47:38 So in the same question cosec of theta
47:41 The value will be 12/7. I tell you so
47:44 Why? What is brother sin theta? p / h and p
47:47 What is the reciprocal of / h? h / p h
47:51 / p So you look at each other p / h / p
47:54 It is reciprocal. p / h / p of each other
47:57 It is reciprocal. so sin theta cosec theta one
48:01 The other is reciprocal. Wait Patience
48:04 Patience, patience, patience. cos theta
48:07 What happens? Base / Hypotenuse. sec
48:10 What is theta? Hypotension/Base. If
48:16 If you pay attention then boss b / h / b / h / p this
48:18 Both are reciprocal of each other
48:20 No? It definitely happens. That's why cos theta
48:23 sec theta are reciprocals of each other.
48:26 I will explain the meaning, wait. tan theta is
48:30 Perpendicular/Base. cot theta is the base
48:35 / Perpendicular. This P / B This P / P This P /
48:37 B These B / P These two are each other's
48:40 It is reciprocal. so tan theta cot theta
48:43 are also reciprocal of each other. Now
48:45 Let me explain what I mean by this
48:48 I want to. If any particular question
48:54 In , assume that the value of tan theta is 5
48:57 / 12 then what is the value of cot theta
49:03 Will you go? 12 / 5 Did you understand? if someone
49:08 The value of sin theta in the question is 5 / 7
49:11 So in the same question, the value of cosec theta
49:14 It will become 7/5.
49:18 If the value of sec theta in a question
49:22 If the value of sec theta is 9 / 4 then
49:25 Reciprocal cos of sec theta in the question
49:28 The value of theta will become 4/9. Why so?
49:32 It's a very simple thing, isn't it? These P / B These B /
49:37 P here P / B here B / P here P / H here H / P here
49:41 B/Sorry this H/B this B/H so easy thing
49:44 Is. So did you understand this? I. Now the second
49:46 thing which should be understood because it is the same
49:49 The thing is that friend, if it is written somewhere that sin
49:52 theta, so you can write that as 1 / cosec theta
49:57 yes. If somewhere it is written cosec theta if
50:00 If it is written somewhere cosec theta then it is 1/
50:03 You can write sin theta simply, why is that so?
50:09 Hey, without looking or not, understand that sin theta is fine.
50:11 Should I make one 1/1? No problem, no problem.
50:14 No, why do I do this, see, I understand now.
50:17 Look up what 1 / cosec theta is cosec
50:20 Theta is h / p now how to solve this
50:23 If you don't understand then first go under the forest.
50:27 Plant a forest. Then put P below H. at the bottom
50:31 These two are at the top among themselves. So P * 1
50:33 P is H, so what is P/H? Look here
50:36 sin theta.
50:38 So that's what I'm trying to say, if somewhere
50:41 It is written sin theta instead of 1 / cosec
50:43 can be written as theta. If it is written somewhere
50:45 cosec theta and write 1 / sin theta instead
50:48 Can. I am saying a very important thing
50:50 Am. Be patient. I know you
50:51 I think I should ask the questions quickly. Bus.
50:52 Bus.
50:55 Listen, every little thing will help.
50:57 Difficult, what did I say, promise me
50:59 You can pick up any other book from the market.
51:01 Your question will become my question.
51:04 Be it the bank or my book or RD Sharma, anyone
51:05 Banana book ho tumhe question bana ye
51:09 I guarantee it. Ok? Just keep watching.
51:12 If it is written cos theta somewhere then instead of it
51:15 You can write 1 / sec theta. if somewhere
51:18 It is written sec theta, so instead of that write 1 / cos
51:19 can be written as theta. what do you understand
51:21 Is it happening? Ok? Because these two are each other
51:23 Reciprocal of. These two belong to each other
51:25 Reciprocal. These two belong to each other
51:30 Reciprocal. Ok? Ok? Is it clear?
51:33 Now another important thing. Now another one
51:35 Important thing. Ok? this is reciprocal
51:37 Identity is established. Now there is one
51:39 Questionable Identity. Now there is one
51:42 Questioning Identity.
51:44 What does it mean? You will understand now. Wet
51:47 do it. Just keep listening. Ok? Question
51:52 I will get it done and clarity will come. now that tan theta
51:56 What happens is that instead of that you use sin theta / cos
51:59 can be written as theta. Why so? I will tell
52:02 Am. Now you see what sin theta is?
52:05 sin theta is perpendicular /
52:08 Hypotension. Yes or no? what is cos theta
52:11 Is? cos theta is the base/hypotenuse.
52:14 Yes or no? Yes sir. It goes up
52:17 Multiply. He goes here. So it came
52:23 Your p*h and here comes your b*h
52:27 How much did the p/b come to and what is p/b
52:29 tan theta
52:33 I am saying the right thing brother, you should think about it.
52:37 what is p / b what is tan theta p / b
52:39 tan theta is in any triangle
52:41 What do I call the ratio of the perpendicular base?
52:46 tan theta and sinθ / cos theta p
52:50 sin theta / cos theta p / b approaching
52:53 Used to be. sinθ / cos theta p / b is approaching.
52:56 So I'll say tan theta. Did you understand the meaning?
53:00 So broadly speaking, you should understand one thing here.
53:03 What should come to mind is that tan theta means
53:06 sin theta / cos theta. That means if you get tan
53:09 If you want to find theta, then sin theta cos theta
53:13 Divide them from each other. And if you
53:16 If we want to find cot theta then cot theta
53:20 The value will be cosθ / sinθ
53:23 Remember these two things.
53:26 This is your questionable identity. Correct
53:28 Is? You will understand how to use it.
53:32 For now, just remember this. Is it clear?
53:35 Ok? Let's move ahead. Now look
53:37 Now the next topic is trigonometric
53:40 Ratios for some specific angles. Right now I
53:42 What am I saying to you? sin theta, sin of
53:45 Angle A, sin of angle C, sin of angle B
53:48 So I'm taking angle A, I'm taking angle X.
53:50 Yes, I am taking theta. any specific angle
53:53 I am not taking whether it is at 0°, 30°, 40°,
53:57 At 45°. Now I'm going to do this. basically
53:59 In this particular part you will understand that
54:02 Boss, what is the value of sin 30°?
54:07 Is? What is the value of sin 60°? tan
54:10 What is the value of 45°? understand what
54:13 I came? Ok? No more remembering values
54:16 Is. You don't have to remember the values. L Miss
54:19 I am getting it done. memorize it within 2 minutes
54:21 Will go. Remember using my technique. Ok?
54:24 Everyone will focus. Everybody Everybody
54:26 Just focus. Ok? Well, here everything
54:29 The values are written. just do one thing
54:31 Are. Let's do one thing. Wait a second. Ok?
54:34 Ok?
54:36 One second. Lalla
54:38 Lalla L
54:40 L
54:49 I erase everything.
54:59 Just look at it, I will remind you. You will enjoy it.
55:02 Ok? Let us go. So the first thing here
55:04 You have to understand that you only have to
55:06 Trigonometric ratios on five angles
55:08 You have to remember the value. just five
55:11 Angles. What are these angles? 0° 30° 45°
55:17 60° 90° 0° 30° 45° 60° 90° 0° 30 45 60
55:21 What is 90 simple mean sin 0°? sin
55:24 What is 30°? What is sin 45°?
55:27 What is sin 60°? what is sin 90°
55:32 Is? cos 0 cos 30 cos 45 cos 60 cos 90
55:35 What happens? Ok? Now watch the start
55:38 We do. Memorization.
55:41 You just need to remember the values of sin.
55:43 You can make everything else instantly and remember it too.
55:46 It will happen gradually. How? I am telling you.
55:48 Look, many teachers will trick you here.
55:50 I will tell you but I will tell you without any tricks.
55:52 I have been. Because you should also remember some trick
55:54 It will have to be done. You will have to remember the trick also.
55:56 I don't believe in any tricks
55:58 In a particular thing. So. Because this without
56:00 The trick is much easier. only of sin
56:03 Remember the values. How?
56:07 sin 0 is zero. sin 30 is 1/2
56:12 sin 45 is 1/2 sin 60 is sin
56:16 60 is 3/2 sin 90 is one bus
56:18 Remember this much, the rest of the table will be remembered automatically.
56:21 Will it happen to remember these five values?
56:25 Will you die brother, remember Zero like this?
56:29 Keep the zero and the one, the zero and the one, this 1/2
56:33 This 1/2 This 3/2 This 1/2 This 1/2 This 3/2
56:36 And if there is a little trick in this which I
56:38 I want to tell you that this is what happens. Don't do anything.
56:40 Zero written here. Wrote one here. Here
56:42 Pay to wrote. Written here three. here
56:46 Wrote four. Divide everything by four. everyone
56:49 Divide it by four. Ok? Everyone from four
56:52 Divided it. And now plant it under the root.
56:55 And now plant it under the root. And now put it on
56:58 What? Under root. What did I say? 0 1 2 3
57:01 4 written. 0 1 2 3 4 written. Everyone from four
57:03 Divide it and install it under the route. whatever answer comes
57:07 Whatever remains is your value. So 0 / 4 0
57:10 It is 0 0. Ok? 1/4 is 1/4 only Will remain.
57:12 Will remain.
57:14 1 is 1. 4
57:16 4
57:19 4 is 2. So this is your 1/2.
57:22 Value. Ok? Now look at 2/4 then 2/4
57:25 How much did it cost? 1/2 1/2
57:27 1 is 1
57:32 2 is 2 so this comes to 1/2.
57:33 It happens to be 3 3
57:34 3
57:38 4 is 2 so it becomes 3/2. 4 / 4 1
57:41 1 is 1, did you understand the point?
57:43 How to remember it? Ok? so that's why
57:45 That's why I told you to remember directly
57:47 Did you tell me to remember it directly? that this
57:52 Zero is 1/2, 1/2 is 3/2, one is simple.
57:54 Now what needs to be done for cos? reverse
57:57 Two. Reverse means write it upside down.
57:59 Write it upside down. I mean here first
58:02 Write one on it.
58:04 You have written one here. Then this one
58:07 Write the value. Then write this one. then this
58:12 Write Wali. Then write this one. Simple. What
58:15 Did you understand? which is the value of your sin 0,
58:18 1/2, 1 / 2, 3 / 2 1 You did it like this
58:22 Gave. I did it like this, I turned it around. Easy. Now tan
58:24 How do you find theta? This is interesting.
58:26 Listen carefully. It is very important. Correct
58:30 Is? Come. Tan 0° has to be found. Isn't it? So
58:35 You should know that tan 0° is
58:37 tan 0° means
58:42 sin 0 / cos 0 yes oh no this is what I taught. tan
58:45 What is theta? sinθ / cosθ yes or
58:49 No? So if tan 0° is to be found then sin 0 /
58:52 cos 0 then sin 0 / cos 0 sin 0 0.
58:57 sin cos 0 is 1. 0 / 1 0 so therefore
59:01 tan 0 is zero. If I ask you tan
59:05 What will be 30°? What will be tan 30°? then tan
59:09 30 means tan 30 / cos 30, understand these things
59:13 It should come now. tan 30 meaning
59:19 sin 30 / cos 30 sin 30 1 / 2 cos 30 3 /
59:23 2 The one below went from the one below, this is your 1 /
59:27 3 How will it come, look here, this is your 1/2
59:32 Your 3/2 this went down to the bottom this is your 1
59:34 / 3 has arrived.
59:37 Now if I ask you to find tan 45
59:42 So tell me tan 45 means sin 45 / cos 45 sin
59:44 45 know cos 45 know divide both
59:48 If you do this, then 45% will come.
59:50 If you divide both of them, then two becomes two.
59:55 How much will it cost 3 will cost 1/0 if you withdraw
59:59 is tan 90° then tan 90 means sin 90 /
60:03 cos 90 sin 90 upon cos 90 sin 901 cos 90 How much is 1 / zero? Friends, any
60:05 How much is 1 / zero? Friends, any If you divide something by zero, it will not
60:07 If you divide something by zero, it will not Defined comes. Infinity doesn't come. Mistake
60:09 Defined comes. Infinity doesn't come. Mistake Do not do it. Not defined. You can't tell
60:11 Do not do it. Not defined. You can't tell What will come? Ok? now cosec theta how
60:14 What will come? Ok? now cosec theta how Will you take it out? cosec 0 to find cosec 0
60:18 Will you take it out? cosec 0 to find cosec 0 Reciprocate sin 0 to find
60:20 Reciprocate sin 0 to find Two. Because I just taught you that
60:22 Two. Because I just taught you that sin theta cosec theta each other
60:24 sin theta cosec theta each other It is reciprocal. Yes and no. these two
60:27 It is reciprocal. Yes and no. these two One is reciprocal of the other. These two are one
60:30 One is reciprocal of the other. These two are one The other is reciprocal. And these two are one
60:33 The other is reciprocal. And these two are one The other is reciprocal. meant to say
60:35 The other is reciprocal. meant to say What? If you reciprocate it, it will be zero.
60:38 What? If you reciprocate it, it will be zero. The reciprocal of 1 / 0 is not
60:41 The reciprocal of 1 / 0 is not Defined. Reciprocal of 1/2 is 2/1 that
60:45 Defined. Reciprocal of 1/2 is 2/1 that The reciprocal of 2 1/2 is 2/1, that is 2
60:50 The reciprocal of 2 1/2 is 2/1, that is 2 3/2 of 2/3 of one is reciprocal one
60:54 3/2 of 2/3 of one is reciprocal one Will remain.
60:56 Will remain. Reciprocal of cos to find sec
60:59 Reciprocal of cos to find sec Reciprocal of 1 3/2 2/3 1/2
61:04 Reciprocal of 1 3/2 2/3 1/2 2 / 1 of 1 / 2 of 2 / 1 Reciprocal of 0
61:08 2 / 1 of 1 / 2 of 2 / 1 Reciprocal of 0 Not Defined
61:10 Not Defined to find cot cot theta
61:12 to find cot cot theta Reciprocal tan theta. So zero
61:15 Reciprocal tan theta. So zero Reciprocal of Not Defined. 1/3 of 3 forest
61:19 Reciprocal of Not Defined. 1/3 of 3 forest 1 of 1 3 of 1 / 3 Reciprocal Got it?
61:24 1 of 1 3 of 1 / 3 Reciprocal Got it? What is the reciprocal of not defined? Not
61:27 What is the reciprocal of not defined? Not Reciprocal of Defined. of Not Defined
61:29 Reciprocal of Defined. of Not Defined Reciprocal means 1 / Not Defined. Brother
61:32 Reciprocal means 1 / Not Defined. Brother Everyone knows that 1/0 is not
61:36 Everyone knows that 1/0 is not Defined. So you think about it, not defined
61:39 Defined. So you think about it, not defined Will come down. Not defined will come down. So 1/
61:41 Will come down. Not defined will come down. So 1/ Not Defined and Zero moved up. to say
61:44 Not Defined and Zero moved up. to say Meaning 1 / Not Defined. of Not Defined
61:47 Meaning 1 / Not Defined. of Not Defined Reciprocal 1 / Not Defined which is Zero
61:49 Reciprocal 1 / Not Defined which is Zero It happens. So this will be your zero. So this
61:52 It happens. So this will be your zero. So this All the values are there. It went by so quickly.
61:55 All the values are there. It went by so quickly. Just remember the values of sinθ. Correct
61:59 Just remember the values of sinθ. Correct Is? Will repeat it once. 0 1/2 1 / 2 3 /
62:03 Is? Will repeat it once. 0 1/2 1 / 2 3 / 2 1 cos that one here 3 / 2 here
62:07 2 1 cos that one here 3 / 2 here 1/2 1/2 0 tan to sin/cos do
62:13 1/2 1/2 0 tan to sin/cos do Two. For cosec, do 1/sin. of sec
62:16 Two. For cosec, do 1/sin. of sec For example, change it to 1 / cos 0. 1 / tan tax for cot
62:18 For example, change it to 1 / cos 0. 1 / tan tax for cot Two. You should remember these values.
62:21 Two. You should remember these values. Ok? Now if you have questions then
62:25 Ok? Now if you have questions then How to do it? Listen carefully once. What
62:27 How to do it? Listen carefully once. What The question of method will interest you in this particular topic.
62:29 The question of method will interest you in this particular topic. Will be asked in. Ok? Now like here
62:31 Will be asked in. Ok? Now like here Look, sin to the power of 460, so first of all, this means
62:34 Look, sin to the power of 460, so first of all, this means I will teach you. Ok? Just look here.
62:36 I will teach you. Ok? Just look here. First the basics. If it is written If it is written
62:40 First the basics. If it is written If it is written sin² theta means sin of theta
62:46 sin² theta means sin of theta Hole Square. Did you understand? If written
62:48 Hole Square. Did you understand? If written is sin² theta so it means sin
62:51 is sin² theta so it means sin Hole square sin theta of theta
62:54 Hole square sin theta of theta Square mean sin theta * sin theta
62:58 Square mean sin theta * sin theta No problem, no problem, but yes, if so
63:01 No problem, no problem, but yes, if so Let it be written sin theta²
63:05 Let it be written sin theta² So that means
63:08 So that means sin theta * is not sin theta
63:14 sin theta * is not sin theta Okay, do you understand this important thing?
63:17 Okay, do you understand this important thing? The thing is
63:18 The thing is square of sinθ square of angle
63:21 square of sinθ square of angle Is. This is the square of the angle. This angle's
63:23 Is. This is the square of the angle. This angle's It is square. So this means sinθ * sin
63:26 It is square. So this means sinθ * sin Theta does not exist.
63:29 Theta does not exist. Ok? Clear thing? Yes. If sin² theta
63:32 Ok? Clear thing? Yes. If sin² theta If it is written then it means the whole of sin theta
63:34 If it is written then it means the whole of sin theta Square means sin theta * sin theta. Correct
63:36 Square means sin theta * sin theta. Correct Is? Now I will explain what I am saying
63:39 Is? Now I will explain what I am saying I want to. Brother, look, I told you about sin.
63:42 I want to. Brother, look, I told you about sin. 460° comfortably. What is sin 60? Brother
63:45 460° comfortably. What is sin 60? Brother What is the meaning of this? This means sin 60
63:49 What is the meaning of this? This means sin 60 to the power of 4 okay so let's write four outside
63:54 to the power of 4 okay so let's write four outside has happened
63:56 has happened What is sin 60? Sin 60 3/2 is
64:01 What is sin 60? Sin 60 3/2 is What is power 4 plus cos 30? cos 30
64:05 What is power 4 plus cos 30? cos 30 How much does it happen? cos is 30
64:10 How much does it happen? cos is 30 sin 60 is equal to 3/2 so this is also 3/2 power 4
64:14 sin 60 is equal to 3/2 so this is also 3/2 power 4 Easy -3 tan 60 what happens if not
64:18 Easy -3 tan 60 what happens if not If you understand then tan 60 means sin 60 / cos 60
64:24 If you understand then tan 60 means sin 60 / cos 60 sin 60 is 3 / 2 cos 60 is 1 /
64:27 sin 60 is 3 / 2 cos 60 is 1 / 2 divided by 2 gives 3, so tan is 60
64:32 2 divided by 2 gives 3, so tan is 60 3 and its square minus tan 45 tan 45
64:36 3 and its square minus tan 45 tan 45 What will happen? sin 45 / cos 45 sin 45 1 / 2
64:42 What will happen? sin 45 / cos 45 sin 45 1 / 2 cos 45 1 / 2 divided by 1 / 2 is 1 / 2 so 1 is left
64:46 cos 45 1 / 2 divided by 1 / 2 is 1 / 2 so 1 is left tan 45 is one and its square plus
64:51 tan 45 is one and its square plus cos 45 should be known so 5 is already written
64:55 cos 45 should be known so 5 is already written cos 45 i.e. 1/2 and its
65:00 cos 45 i.e. 1/2 and its Square it and solve it easily by 3.
65:04 Square it and solve it easily by 3. Power 4 if not known then 3 * 3 * 3 * 3
65:10 Power 4 if not known then 3 * 3 * 3 * 3 This is what is meant by 4 to the power of. So 3 * 3 3 * 3
65:15 This is what is meant by 4 to the power of. So 3 * 3 3 * 3 3 * 3 = 9 so 3 to the power of 4 is 9
65:21 3 * 3 = 9 so 3 to the power of 4 is 9 How much did it cost? 9 2 power 4 of 16 plus 3
65:26 How much did it cost? 9 2 power 4 of 16 plus 3 2 to the power 4 is 9. 2 to the power 4 is 16, right? And
65:30 2 to the power 4 is 9. 2 to the power 4 is 16, right? And There is a four outside your place. Correct
65:33 There is a four outside your place. Correct Is? - of 3 3² 3 1² 1 + 5 1² 1 2² 2 EG
65:43 Is? - of 3 3² 3 1² 1 + 5 1² 1 2² 2 EG So here you go, 9 + 9 + 9 is 18.
65:49 So here you go, 9 + 9 + 9 is 18. 16 Your four is written outside. - 3 * 2 +
65:56 16 Your four is written outside. - 3 * 2 + 5 / 2 so this is 4
65:59 5 / 2 so this is 4 Ok? 2 * 2 * 9 So here you go 9 / 2
66:05 Ok? 2 * 2 * 9 So here you go 9 / 2 + 5 / 2 - 6 / 1 Clear? Okay, right?
66:11 + 5 / 2 - 6 / 1 Clear? Okay, right? If it is basic maths then you will know LCM.
66:14 If it is basic maths then you will know LCM. to here na here 5 because to to
66:17 to here na here 5 because to to It is installed here. what is here in the forest
66:18 It is installed here. what is here in the forest Should I multiply? 2 / 2 so 2 * 6 = 12
66:22 Should I multiply? 2 / 2 so 2 * 6 = 12 9 + 5 14 - 12 is 2 / 2 that is one answer
66:28 9 + 5 14 - 12 is 2 / 2 that is one answer Gaya forest.
66:30 Gaya forest. Easy, you will also be asked basic questions like this.
66:33 Easy, you will also be asked basic questions like this. They go and ask what? CBSE
66:36 They go and ask what? CBSE CBSE asked this question in 2025
66:41 CBSE asked this question in 2025 Had gone. Very simple. Ok? Let us go. So
66:44 Had gone. Very simple. Ok? Let us go. So Bhai saheb CBSE 2025 paper a little
66:46 Bhai saheb CBSE 2025 paper a little It is called a difficult paper. This over there
66:48 It is called a difficult paper. This over there The question came up. Okay, right? so such
66:50 The question came up. Okay, right? so such In between you will get CBSE 2025 questions
66:52 In between you will get CBSE 2025 questions I will show you because that paper was called difficult.
66:54 I will show you because that paper was called difficult. Had gone. And you will see how easily you
66:55 Had gone. And you will see how easily you Those questions will be made from this. Ok? Let us go
66:57 Those questions will be made from this. Ok? Let us go Boss. So it is simple. What is sin 30?
67:00 Boss. So it is simple. What is sin 30? What is sin 30?
67:03 What is sin 30? What is 1 / 2 - 4 sin 30? 1/2 of
67:09 What is 1 / 2 - 4 sin 30? 1/2 of Cube divided by sin 50° brother. sin
67:14 Cube divided by sin 50° brother. sin 50 cos 50
67:17 50 cos 50 I don't even know the value of sin 50. cos 50
67:19 I don't even know the value of sin 50. cos 50 I don't even know its value. How is this
67:21 I don't even know its value. How is this Will I take it out then? Don't take tension.
67:24 Will I take it out then? Don't take tension. I will tell you this in a while. Correct
67:27 I will tell you this in a while. Correct Is? Why did I bring you here now?
67:29 Is? Why did I bring you here now? Did you get this question? I can show you this
67:31 Did you get this question? I can show you this If you look at this question,
67:33 If you look at this question, This concept will come to your mind that
67:35 This concept will come to your mind that I know sin 30 and I know cos sin 30.
67:37 I know sin 30 and I know cos sin 30. I will keep the value. You already know sin 50 cos 50
67:40 I will keep the value. You already know sin 50 cos 50 No. What will I do with it? wait a while
67:42 No. What will I do with it? wait a while Lala. I will teach you then. Don't worry. Ok?
67:45 Lala. I will teach you then. Don't worry. Ok? Please wait a little for this question. This
67:47 Please wait a little for this question. This I'll save it for later. Ok? Let us go
67:50 I'll save it for later. Ok? Let us go So let's ask another question. This one is simple
67:53 So let's ask another question. This one is simple EGYPT 11TH QUEEN. The value of cos 60
67:57 EGYPT 11TH QUEEN. The value of cos 60 What is the value of cos 60? cos 60
68:00 What is the value of cos 60? cos 60 Is. Use your brain. cos 60 is your 1 /
68:03 Is. Use your brain. cos 60 is your 1 / 2 squared and your five written outside
68:06 2 squared and your five written outside Is. plus sec 30 sec 30 is cos 30
68:10 Is. plus sec 30 sec 30 is cos 30 Reciprocal. So what is cos 30 brother?
68:15 Reciprocal. So what is cos 30 brother? What is cos 30? 3 / 2 so sec 30
68:19 What is cos 30? 3 / 2 so sec 30 What will happen? 2 / 3 Simple. Ok? So
68:23 What will happen? 2 / 3 Simple. Ok? So sec 30 became your 2/3 and his
68:27 sec 30 became your 2/3 and his Square and outside off, a four is placed. tan 45
68:31 Square and outside off, a four is placed. tan 45 sin 45 / cos 45 that is one so this is your 1²
68:36 sin 45 / cos 45 that is one so this is your 1² divided by sin squared of 30 1/2
68:40 divided by sin squared of 30 1/2 cos 30
68:42 cos 30 1 /
68:44 1 / Sorry
68:46 Sorry 3/2²
68:49 3/2² Ok? Solve it easily. So here it is 5*
68:55 Ok? Solve it easily. So here it is 5* 1 / 4 + 4 * 2² 4 3² 3 - 1 / 1
69:04 1 / 4 + 4 * 2² 4 3² 3 - 1 / 1 Divided by 1 square 1 2² 4 3² 3 2² 4
69:09 Divided by 1 square 1 2² 4 3² 3 2² 4 Solve it. So your score is 5/4.
69:14 Solve it. So your score is 5/4. + 16 / 3 - 1 / 1 if you look below carefully
69:18 + 16 / 3 - 1 / 1 if you look below carefully So from 1 + 3 4 / 4 1 so down comes your one
69:23 So from 1 + 3 4 / 4 1 so down comes your one Went. There is no need to write. to this very
69:25 Went. There is no need to write. to this very Solve it. Solve this only. So this
69:29 Solve it. Solve this only. So this Your answer is 4, LCM of 3 and 1 is 12.
69:32 Your answer is 4, LCM of 3 and 1 is 12. Will go.
69:34 Will go. The LCM of 4 3 and 1 is 12. What's in Four
69:37 The LCM of 4 3 and 1 is 12. What's in Four Should I multiply? 12 / 3 so 3 * 5 15 three
69:41 Should I multiply? 12 / 3 so 3 * 5 15 three what should I multiply 12 / 4 so 16 *
69:45 what should I multiply 12 / 4 so 16 * 4 = 64 what should I multiply in one 12 /
69:49 4 = 64 what should I multiply in one 12 / 12 will come here minus 12 okay
69:52 12 will come here minus 12 okay So 64 - 12 is 52
69:57 So 64 - 12 is 52 52 + 15 is 67
70:00 52 + 15 is 67 / 12 Your final answer. 67/12
70:04 / 12 Your final answer. 67/12 Your final answer is coming.
70:07 Your final answer is coming. Ok? This method gives you trigonometric
70:10 Ok? This method gives you trigonometric Ratios for some specific angle questions
70:12 Ratios for some specific angle questions Questions will be asked at the basic level. Ok? Now this
70:15 Questions will be asked at the basic level. Ok? Now this But what makes for better questions? That
70:18 But what makes for better questions? That But let's talk about it once. very simple
70:20 But let's talk about it once. very simple Cheese tell me one thing everyone. If here
70:23 Cheese tell me one thing everyone. If here and sinθ = sinθ = is written
70:29 and sinθ = sinθ = is written 1/2.
70:31 1/2. If sinθ is written as 1/2, tell using common sense.
70:35 If sinθ is written as 1/2, tell using common sense. What will be the value of theta? think about it
70:39 What will be the value of theta? think about it Think about it. Think about it, think about it.
70:41 Think about it. Think about it, think about it. If it is written sin theta, the value of sin theta is 1/2 theta
70:44 If it is written sin theta, the value of sin theta is 1/2 theta What will happen? It must have come to your mind
70:46 What will happen? It must have come to your mind What brother? At what angle is sin equal to 1/2?
70:49 What brother? At what angle is sin equal to 1/2? Is? At what angle is sin equal to 1/2? 30°
70:52 Is? At what angle is sin equal to 1/2? 30° But. So the value of theta comes to 30°.
70:56 But. So the value of theta comes to 30°. Easy? Easy. Any problem? so theta you
71:00 Easy? Easy. Any problem? so theta you Write 30 directly or it would have to be done like this
71:02 Write 30 directly or it would have to be done like this Is. Look at this sinθ 1/2 sin where
71:06 Is. Look at this sinθ 1/2 sin where It happens? at sin 30. So here you are
71:11 It happens? at sin 30. So here you are You write that on comparison, everyone should pay attention
71:14 You write that on comparison, everyone should pay attention Log on comparison, don't do that sin to sin
71:17 Log on comparison, don't do that sin to sin Let it be cut. Doesn't happen like this. from sin to sin then
71:20 Let it be cut. Doesn't happen like this. from sin to sin then When this sin * theta and this sin * 30 intersect
71:25 When this sin * theta and this sin * 30 intersect Would. And I taught you how to start
71:27 Would. And I taught you how to start in that sin theta does not mean sin * theta
71:29 in that sin theta does not mean sin * theta It happens. Ok? So on comparison, I mean brother
71:34 It happens. Ok? So on comparison, I mean brother Theta is your 30 if you compare both sides.
71:37 Theta is your 30 if you compare both sides. Do theta and you'll get 30°. Let's have another one
71:39 Do theta and you'll get 30°. Let's have another one question if I ask you guys if I
71:42 question if I ask you guys if I I ask you guys that tan
71:46 I ask you guys that tan x = tan x = coming coming coming
71:51 x = tan x = coming coming coming Suppose 3
71:54 Suppose 3 So what will be the value of x? tan which
71:57 So what will be the value of x? tan which Is there 3 on the angle? At what angle is tan 3
72:00 Is there 3 on the angle? At what angle is tan 3 It happens? At 60. So x is your 60. Correct
72:03 It happens? At 60. So x is your 60. Correct Is? So you have to do it in such a way that who is tan
72:06 Is? So you have to do it in such a way that who is tan 3 at an angle from? at tan 60. But instead of 3
72:09 3 at an angle from? at tan 60. But instead of 3 tan 60 3 instead of tan 60 and written here
72:12 tan 60 3 instead of tan 60 and written here On comparison, if you compare both sides
72:15 On comparison, if you compare both sides Brother, when will both sides become equal?
72:17 Brother, when will both sides become equal? If it is 60 here then tan 60 tan 60 means x
72:21 If it is 60 here then tan 60 tan 60 means x Your 60 has arrived.
72:24 Your 60 has arrived. Ok? You would have been asked more such questions.
72:27 Ok? You would have been asked more such questions. Are. This was a very basic level. Come a little
72:29 Are. This was a very basic level. Come a little I will get it done at a good level. What did you say now?
72:32 I will get it done at a good level. What did you say now? Read the question comfortably. Solve Etch
72:34 Read the question comfortably. Solve Etch of the following equations for theta. Good
72:37 of the following equations for theta. Good By the way you are studying trigonometry
72:39 By the way you are studying trigonometry Right now you are reading between zero and 90°.
72:41 Right now you are reading between zero and 90°. Or at zero and 90. Isn't it? Class
72:44 Or at zero and 90. Isn't it? Class Things are different in 11th. like anyway
72:48 Things are different in 11th. like anyway Read this given to you carefully first. 2 *
72:52 Read this given to you carefully first. 2 * cos 3 theta = 1 important thing is this angle
72:55 cos 3 theta = 1 important thing is this angle Is. This is the angle. This is the angle. This is the angle.
72:59 Is. This is the angle. This is the angle. This is the angle. This is the angle. There is an angle. There is an angle. angle's
73:02 This is the angle. There is an angle. There is an angle. angle's What does it mean? Don't make the mistake of being very
73:05 What does it mean? Don't make the mistake of being very What do all the children do? Let's assume that
73:08 What do all the children do? Let's assume that It is written like this, suppose it is written like this cos 3
73:10 It is written like this, suppose it is written like this cos 3 theta = 1 Many children make this mistake
73:14 theta = 1 Many children make this mistake They say that it is written like this, so cos
73:16 They say that it is written like this, so cos Let's make theta 1/3. take down three
73:19 Let's make theta 1/3. take down three Went.
73:21 Went. This mistake should not be made. This is Angle's. These
73:24 This mistake should not be made. This is Angle's. These It is of angle. This angle of his is moving along
73:26 It is of angle. This angle of his is moving along Is. He is moving along. He walks along
73:28 Is. He is moving along. He walks along Used to be. Do you understand the point of what I am saying?
73:30 Used to be. Do you understand the point of what I am saying? Have I been? Okay, right? This is the 3 theta angle.
73:33 Have I been? Okay, right? This is the 3 theta angle. Complete. Don't turn down the three. Yes.
73:36 Complete. Don't turn down the three. Yes. But if it were written that three
73:39 But if it were written that three Hey, the board is stuck. gets wet for a minute
73:42 Hey, the board is stuck. gets wet for a minute It is sometimes. Yes sir. So now if it is written like this
73:45 It is sometimes. Yes sir. So now if it is written like this Listen carefully. But suppose if so
73:47 Listen carefully. But suppose if so It is written that 3 * cos θ = 1 / θ = 1, then
73:53 It is written that 3 * cos θ = 1 / θ = 1, then You can take this three down there.
73:56 You can take this three down there. Reese three now in multiplication three now
73:59 Reese three now in multiplication three now In multiplication, whatever
74:01 In multiplication, whatever If it is multiplication then it will go into division.
74:03 If it is multiplication then it will go into division. Did you understand? Now you are asked what is theta's
74:07 Did you understand? Now you are asked what is theta's Tell me the value. What is the value of theta? Correct
74:09 Tell me the value. What is the value of theta? Correct Is? And this is given to you first.
74:12 Is? And this is given to you first. By completely isolating the trigonometric ratios
74:14 By completely isolating the trigonometric ratios Two. Now cos 3θ is written as 2. So
74:18 Two. Now cos 3θ is written as 2. So What did you do? cos 3a = 1 / 2.
74:22 What did you do? cos 3a = 1 / 2. So the trigonometric ratios are different.
74:24 So the trigonometric ratios are different. It got separated there. Now cos is which angle?
74:27 It got separated there. Now cos is which angle? But at what angle is cos equal to 1/2? These
74:29 But at what angle is cos equal to 1/2? These See. At what angle is cos 1/2?
74:34 See. At what angle is cos 1/2? Check the table if you don't remember. cos
74:38 Check the table if you don't remember. cos At 60° it is 1/2. So instead of 1/2 cos 60
74:43 At 60° it is 1/2. So instead of 1/2 cos 60 Write cos 60 instead of 1/2 cos 60 instead of 1/2
74:47 Write cos 60 instead of 1/2 cos 60 instead of 1/2 Gave. Now compare both the sides. Now
74:51 Gave. Now compare both the sides. Now Compare both sides. cos cos cos
74:53 Compare both sides. cos cos cos cos so equals 3 theta 60 so 3 theta 60
74:59 cos so equals 3 theta 60 so 3 theta 60 equals to theta 60 / 3 so theta 20
75:04 equals to theta 60 / 3 so theta 20 equal and you can also check that when the boss
75:08 equal and you can also check that when the boss If you write 20 here then 20 * 3 = 60
75:11 If you write 20 here then 20 * 3 = 60 cos 60 is equal to cos 60 basically what does it mean
75:14 cos 60 is equal to cos 60 basically what does it mean what should I put in place of theta so that both
75:17 what should I put in place of theta so that both What should I put in place of side equal to theta
75:19 What should I put in place of side equal to theta Both sides are equal, so theta is 20.
75:20 Both sides are equal, so theta is 20. If you put it, cos 60 will be equal to cos 60.
75:22 If you put it, cos 60 will be equal to cos 60. Will go. Similarly, what will you do here brother?
75:25 Will go. Similarly, what will you do here brother? Firstly sin 2θ = 3 / 2 Now sin which
75:31 Firstly sin 2θ = 3 / 2 Now sin which What is the angle at which 3/2? sin which angle
75:34 What is the angle at which 3/2? sin which angle But what is 3/2? at sin 60°. So 3/2
75:38 But what is 3/2? at sin 60°. So 3/2 Now if you subtract both sides of sin 60
75:42 Now if you subtract both sides of sin 60 If you compare, your 2 theta is equal to 60.
75:46 If you compare, your 2 theta is equal to 60. So your theta is equal to 30. Now check it
75:50 So your theta is equal to 30. Now check it Brother. What would you write in place of theta so that
75:53 Brother. What would you write in place of theta so that Both sides should be equal. 30 because 30 * 2
75:56 Both sides should be equal. 30 because 30 * 2 = 60 sin 60 sin 60 equals.
76:00 = 60 sin 60 sin 60 equals. Don't take these five down here. angle
76:03 Don't take these five down here. angle That's five inside the angle of. So here
76:06 That's five inside the angle of. So here What will you do? tan 5 theta tan which
76:09 What will you do? tan 5 theta tan which At an angle? tan at which angle? tan which
76:12 At an angle? tan at which angle? tan which Is there a forest at an angle? at tan 45. instead of 1
76:15 Is there a forest at an angle? at tan 45. instead of 1 tan 45 and now if you compare both sides
76:18 tan 45 and now if you compare both sides If you do it, it should be 45 here also. Meaning
76:21 If you do it, it should be 45 here also. Meaning 45 instead of 5 theta, so your theta is 9 you
76:28 45 instead of 5 theta, so your theta is 9 you See, when you write nine here, you get 5*
76:30 See, when you write nine here, you get 5* 9 = 45 tan 45 tan 45 equals
76:34 9 = 45 tan 45 tan 45 equals Easy.
76:36 Easy. Ok? Now let's look at another question based on this.
76:39 Ok? Now let's look at another question based on this. just. Ok? Many questions based on this
76:41 just. Ok? Many questions based on this Let's come. Very cute, almost all of them
76:43 Let's come. Very cute, almost all of them I will get all the questions done. Don't take the load. you
76:46 I will get all the questions done. Don't take the load. you Just keep watching and doing it with me. Correct
76:47 Just keep watching and doing it with me. Correct Is? what did you say? Find the value of x and
76:50 Is? what did you say? Find the value of x and You are given that 2sin
76:53 You are given that 2sin x / 2 equals 1. Remember that inside sin
76:56 x / 2 equals 1. Remember that inside sin It is written that is his angle. which is inside the sin
76:59 It is written that is his angle. which is inside the sin It is written that is his angle. Ok? this mistake
77:01 It is written that is his angle. Ok? this mistake Don't do that take two up. because this angle
77:04 Don't do that take two up. because this angle Is. This is the angle. This is the complete angle.
77:07 Is. This is the angle. This is the complete angle. Ok? What did I say first?
77:10 Ok? What did I say first? Differentiate the trigonometric ratios. So to
77:13 Differentiate the trigonometric ratios. So to It is written so this 1/2 now sin which angle
77:16 It is written so this 1/2 now sin which angle But 1/2? At what angle is sin 1/2? sin
77:21 But 1/2? At what angle is sin 1/2? sin at 30° then sin 30 is 1/2 sin 30 is 1/2
77:26 at 30° then sin 30 is 1/2 sin 30 is 1/2 It happens. So instead of 1/2 sin 30 instead of 1/2
77:29 It happens. So instead of 1/2 sin 30 instead of 1/2 sin 30 Now you see if you look at both sides
77:32 sin 30 Now you see if you look at both sides Compare then x/2 and 30 are equal
77:36 Compare then x/2 and 30 are equal Needed So x/2 equals 30 x your 60
77:41 Needed So x/2 equals 30 x your 60 Equally, and this is true. Why? If you x
77:44 Equally, and this is true. Why? If you x If you write 60 instead of 30 then it will be 60 / 230 sin 30 sin
77:47 If you write 60 instead of 30 then it will be 60 / 230 sin 30 sin 30 times x is equal to 60.
77:51 30 times x is equal to 60. Easy. Ok? And just look. Ok? this is
77:54 Easy. Ok? And just look. Ok? this is I'll get you done later. as
77:56 I'll get you done later. as I told you. Be patient. Let's go, this one
77:59 I told you. Be patient. Let's go, this one Question. Ok? Relax, relax. Now we
78:02 Question. Ok? Relax, relax. Now we What are people asking questions about?
78:03 What are people asking questions about? Trigonometric Ratios for Some Specific
78:05 Trigonometric Ratios for Some Specific Doing it at an angle. what did you say? Find the
78:07 Doing it at an angle. what did you say? Find the Value of x. Something like this is a given. I
78:09 Value of x. Something like this is a given. I what did you say? Differentiating Trigonometric Ratios
78:12 what did you say? Differentiating Trigonometric Ratios Have to do it. Differentiating Trigonometric Ratios
78:14 Have to do it. Differentiating Trigonometric Ratios First thing to do. Ok? So here
78:15 First thing to do. Ok? So here There is also sin x, there is also cos x. friend two
78:17 There is also sin x, there is also cos x. friend two Trigonometric ratios arrived. Easy.
78:20 Trigonometric ratios arrived. Easy. First separate it. So it is written here
78:23 First separate it. So it is written here 3 * sin x and here it is written cos x *
78:27 3 * sin x and here it is written cos x * 1 can speak. Or I can write it as 1 * cos
78:30 1 can speak. Or I can write it as 1 * cos Let me say x. Is there any problem? Hey One
78:32 Let me say x. Is there any problem? Hey One If you multiply anything by 1 * cos cos
78:35 If you multiply anything by 1 * cos cos Only x will come. Now for trigonometry
78:37 Only x will come. Now for trigonometry How to differentiate the ratio? under sin x
78:40 How to differentiate the ratio? under sin x cos x how? Anything with Forest
78:42 cos x how? Anything with Forest Will come down to multiplication. sin of x
78:45 Will come down to multiplication. sin of x With 3 will come down in multiplication.
78:48 With 3 will come down in multiplication. Now what is sin x / cos x? tan x tan
78:53 Now what is sin x / cos x? tan x tan x 1 / 3 Now you understand. tan which angle
78:57 x 1 / 3 Now you understand. tan which angle But what happens to 1/3? At what angle tan 1/
79:01 But what happens to 1/3? At what angle tan 1/ Is it 3? at tan 30. So instead of 1/3, tan
79:04 Is it 3? at tan 30. So instead of 1/3, tan 30 So on comparison if you look at x your
79:08 30 So on comparison if you look at x your 30 has arrived. x Your 30 has arrived.
79:12 30 has arrived. x Your 30 has arrived. Easy next very cute question.
79:16 Easy next very cute question. This question has come many times in CBSE.
79:19 This question has come many times in CBSE. Focus and see. Put a star, brother.
79:22 Focus and see. Put a star, brother. Or write hashtag cute. hashtag
79:25 Or write hashtag cute. hashtag QT Question. Ok? Acuity
79:27 QT Question. Ok? Acuity I call such questions questions.
79:29 I call such questions questions. Come on, what are you saying? If a and b are
79:31 Come on, what are you saying? If a and b are Acute angles. I will say it again as much as
79:33 Acute angles. I will say it again as much as Do as much as you can from your side. Answer
79:34 Do as much as you can from your side. Answer It keeps coming. if a and b are acute
79:37 It keeps coming. if a and b are acute Angles mean a and b are units. means a and b
79:40 Angles mean a and b are units. means a and b The value of both is less than 90. Acute
79:43 The value of both is less than 90. Acute This is what angle means. Ok? true that
79:45 This is what angle means. Ok? true that True that sin a - b 0 is given. Fear
79:49 True that sin a - b 0 is given. Fear Not there. What is given? what has been given
79:52 Not there. What is given? what has been given Is? sin a - b means this is the complete angle of sin
79:56 Is? sin a - b means this is the complete angle of sin Is. Sin is zero at some angle. sin someone
79:59 Is. Sin is zero at some angle. sin someone Zero in on the angle. sin at any angle zero. sin
80:02 Zero in on the angle. sin at any angle zero. sin Zero at some angle. Ok? given like this
80:03 Zero at some angle. Ok? given like this Is. What else have you given? 2 cos a + b – 1 = 0
80:08 Is. What else have you given? 2 cos a + b – 1 = 0 So 2 cos
80:11 So 2 cos a + b - 1 = 0 and tell you to find angles
80:16 a + b - 1 = 0 and tell you to find angles a and b now tell me if you have any idea about two things
80:20 a and b now tell me if you have any idea about two things Finding the value of is called maths
80:22 Finding the value of is called maths So how many equations do you have?
80:24 So how many equations do you have? There should be two equations, yes or no.
80:26 There should be two equations, yes or no. Are you there with me guys should be fine too
80:29 Are you there with me guys should be fine too Isn't it, let's go then
80:32 Isn't it, let's go then So
80:34 So If you calculate the value of two variables, then two
80:36 If you calculate the value of two variables, then two There should be equations. I have two
80:38 There should be equations. I have two There are equations but here a and b are just
80:41 There are equations but here a and b are just Not there. Sin and cos are also applied. Rest
80:43 Not there. Sin and cos are also applied. Rest From
80:45 From Sin is zero at some angle. sin which brother?
80:50 Sin is zero at some angle. sin which brother? This is the angle of sin. Brother, this is the angle.
80:53 This is the angle of sin. Brother, this is the angle. of cos. So at what angle is sin zero?
80:56 of cos. So at what angle is sin zero? At what angle is sin zero? at sin 0.
80:59 At what angle is sin zero? at sin 0. So instead of zero I wrote sin 0. If here
81:03 So instead of zero I wrote sin 0. If here But if 1/2 was written then sin 30 would have been written. If
81:06 But if 1/2 was written then sin 30 would have been written. If 3/2 would be written as sin 60. If 1/2 then sin 45
81:09 3/2 would be written as sin 60. If 1/2 then sin 45 I would write. Where does 0 occur? at sin 0. So
81:11 I would write. Where does 0 occur? at sin 0. So Wrote sin 0 instead of zero. Now the benefit
81:13 Wrote sin 0 instead of zero. Now the benefit What? If you compare both sides.
81:17 What? If you compare both sides. Compare both sides, so sin sin a - b 0
81:21 Compare both sides, so sin sin a - b 0 Equal to. Do you understand what I am saying?
81:23 Equal to. Do you understand what I am saying? a - b equals 0. And this is your equation.
81:27 a - b equals 0. And this is your equation. Is. This is your equation. now over here
81:30 Is. This is your equation. now over here First, separate the trigonometric ratios.
81:32 First, separate the trigonometric ratios. have to do it. How will you separate it? See. So 2
81:34 have to do it. How will you separate it? See. So 2 cos of angle
81:38 cos of angle = 1 How? -1 If I went there, it was forest. cos of angle
81:45 = 1 How? -1 If I went there, it was forest. cos of angle 1/2. then the trigonometric ratios are different
81:48 1/2. then the trigonometric ratios are different Went. cos of angle. Now at what angle is cos
81:50 Went. cos of angle. Now at what angle is cos Is it 1/2?
81:53 Is it 1/2? At what angle is cos 1/2? cos 60
81:56 At what angle is cos 1/2? cos 60 But. So cos 60 instead of 1/2 now if you both
82:01 But. So cos 60 instead of 1/2 now if you both Compare the sides so cos cos a + b is 60
82:06 Compare the sides so cos cos a + b is 60 Equal to. a + b equals 60. How easy
82:09 Equal to. a + b equals 60. How easy Is. a + b equals 60. This is your second
82:12 Is. a + b equals 60. This is your second Equation. and two variables, two equations
82:15 Equation. and two variables, two equations Every child knows how to solve it. This
82:17 Every child knows how to solve it. This I don't know. I will tell you once. So
82:19 I don't know. I will tell you once. So Look boss. a - b 0
82:24 Look boss. a - b 0 and a + b 60
82:27 and a + b 60 I can solve both the equations using the elimination method.
82:31 I can solve both the equations using the elimination method. I'll plus or minus a variable
82:33 I'll plus or minus a variable Eliminate will I do plus. Let's if
82:35 Eliminate will I do plus. Let's if So I'm adding both equations together.
82:37 So I'm adding both equations together. There will be no sign change. So a + a 2a
82:41 There will be no sign change. So a + a 2a - b + b cut 0 + 60 60 so 2a = 60 a
82:46 - b + b cut 0 + 60 60 so 2a = 60 a Yours is 30° and if a 30 is any
82:51 Yours is 30° and if a 30 is any If you replace a with 30 in an equation, then b
82:56 If you replace a with 30 in an equation, then b will also come - if b went there then b will also come your 30
83:00 will also come - if b went there then b will also come your 30 Went. a 30 b 30 a 30 b 30 is your correct
83:05 Went. a 30 b 30 a 30 b 30 is your correct Answer. And you can also check that 30 30 -
83:09 Answer. And you can also check that 30 30 - 30 0 sin 0 is 0. Look here 30+
83:13 30 0 sin 0 is 0. Look here 30+ 30 cos 60, right? So you see 2 * cos 60
83:18 30 cos 60, right? So you see 2 * cos 60 - 1 will equal 0.
83:22 - 1 will equal 0. Ok? This way you will get these questions
83:25 Ok? This way you will get these questions Are asked. Now, as trigonometry
83:28 Are asked. Now, as trigonometry I told you trigonometry is science.
83:30 I told you trigonometry is science. of Measuring Triangles. Meaning
83:32 of Measuring Triangles. Meaning In trigonometry you people are looking for right angles.
83:34 In trigonometry you people are looking for right angles. Let's measure the triangle. Meaning
83:36 Let's measure the triangle. Meaning Looking at the angles and sides of the triangle
83:39 Looking at the angles and sides of the triangle Are. Look at this question a lot.
83:41 Are. Look at this question a lot. Easy. In triangle PQR a triangle PQR
83:45 Easy. In triangle PQR a triangle PQR Right angle at Q. Ok? So as much as I understand
83:47 Right angle at Q. Ok? So as much as I understand Let's do as much as we can. So he told us
83:49 Let's do as much as we can. So he told us What clearly? That is a triangle PQR. Correct
83:51 What clearly? That is a triangle PQR. Correct Is? We were told that there is a triangle PQR. Correct
83:55 Is? We were told that there is a triangle PQR. Correct Is? Why left right angle right? Right on Q
83:58 Is? Why left right angle right? Right on Q There is an angle. is at right angle to Q. Ok? PQ3
84:02 There is an angle. is at right angle to Q. Ok? PQ3 is given. So clearly PQ3 is given.
84:05 is given. So clearly PQ3 is given. PR 6 is given. What is the matter?
84:08 PR 6 is given. What is the matter? Determine angle P and R Determine angle P
84:11 Determine angle P and R Determine angle P and R to ask you to find angle P and angle R
84:15 and R to ask you to find angle P and angle R It has been said. You can also find angle P and angle R.
84:18 It has been said. You can also find angle P and angle R. To take out. Angle P and angle R give you
84:20 To take out. Angle P and angle R give you Have to take it out.
84:22 Have to take it out. Ok? How to do this friend? So I don't understand
84:25 Ok? How to do this friend? So I don't understand Something is coming. I tell you. Dude first of all
84:28 Something is coming. I tell you. Dude first of all You are understanding one thing that right angle
84:30 You are understanding one thing that right angle It is a triangle. Correct? Correct? So Pythagoras
84:33 It is a triangle. Correct? Correct? So Pythagoras The theorem comes to mind. what do you do with it
84:36 The theorem comes to mind. what do you do with it Can you? To do it or not to do it is a different matter.
84:37 Can you? To do it or not to do it is a different matter. The thing is. But what can you do? if these
84:39 The thing is. But what can you do? if these If you have given three or six then you can do this very easily.
84:42 If you have given three or six then you can do this very easily. You can also extract QR. Ok?
84:44 You can also extract QR. Ok? But if I tell you all to listen
84:47 But if I tell you all to listen People be careful. If I speak to you people
84:50 People be careful. If I speak to you people Listen carefully for this angle. this angle
84:54 Listen carefully for this angle. this angle Base and perpendicular and hypo for what?
84:57 Base and perpendicular and hypo for what? So for this angle, this base, this hypo
85:03 So for this angle, this base, this hypo This is perpendicular but that is not given.
85:05 This is perpendicular but that is not given. I will leave him. Now you all me
85:08 I will leave him. Now you all me Can you tell me if I can write like this? Base
85:13 Can you tell me if I can write like this? Base and hypo. What is the ratio of base and hypo?
85:16 and hypo. What is the ratio of base and hypo? Is? Base and hypo sorry base and hypo ones
85:20 Is? Base and hypo sorry base and hypo ones What do I call the ratio?
85:21 What do I call the ratio? In trigonometry?
85:23 In trigonometry? base hypocos so can I say that
85:27 base hypocos so can I say that cos of angle p cos of angle p base /
85:32 cos of angle p cos of angle p base / It is hypo, can I say that
85:35 It is hypo, can I say that Listen carefully to cos cos of angle p base /
85:39 Listen carefully to cos cos of angle p base / Hearing hypotonus and bass
85:43 Hearing hypotonus and bass And the base is given to you, three hypos are given to you
85:47 And the base is given to you, three hypos are given to you is six so cos of angle p 1 / 2 cos which
85:52 is six so cos of angle p 1 / 2 cos which The angle from is 1/2. cos which
85:55 The angle from is 1/2. cos which What is the angle at which 1/2? at cos 60. cos
85:59 What is the angle at which 1/2? at cos 60. cos At which angle is 1/2 cos 60.
86:04 At which angle is 1/2 cos 60. On Comparison
86:06 On Comparison p Your 60 has arrived. I tell you to remove P.
86:10 p Your 60 has arrived. I tell you to remove P. Were living. P Your 60 has arrived. you understand me
86:13 Were living. P Your 60 has arrived. you understand me What am I saying? Didn't you understand? Something
86:15 What am I saying? Didn't you understand? Something No. left it. Let's do one thing. One
86:19 No. left it. Let's do one thing. One Let's work. Hear Patience
86:22 Let's work. Hear Patience Absolute patience. This is your P. Let us go
86:24 Absolute patience. This is your P. Let us go Let me take this angle. to this angle
86:26 Let me take this angle. to this angle Just tell me everybody, what is this angle?
86:30 Just tell me everybody, what is this angle? What will this be for? What will this be? Just this
86:32 What will this be for? What will this be? Just this Tell me. So for this angle, this
86:35 Tell me. So for this angle, this It will be perpendicular and it will be hypotensive.
86:40 It will be perpendicular and it will be hypotensive. Now tell me perpendicular and hypotenuse
86:43 Now tell me perpendicular and hypotenuse What do I call the ratio?
86:46 What do I call the ratio? sin. So sin of angle r if I tell you guys
86:50 sin. So sin of angle r if I tell you guys What will be the sin of angle r? So
86:53 What will be the sin of angle r? So perpendicular
86:55 perpendicular / What is the hypotenuse i.e. sin of angle r
86:58 / What is the hypotenuse i.e. sin of angle r Will you go? What is 3/6 i.e. sin of angle r
87:03 Will you go? What is 3/6 i.e. sin of angle r Will you go? At what angle is 1/2 sin 1/2
87:07 Will you go? At what angle is 1/2 sin 1/2 It happens? At what angle is sin equal to 1/2?
87:10 It happens? At what angle is sin equal to 1/2? Is? at sin 30. So on comparison
87:15 Is? at sin 30. So on comparison On Comparison R Your 30 has arrived. This is your 30
87:19 On Comparison R Your 30 has arrived. This is your 30 I have arrived. I only asked you to remove R.
87:22 I have arrived. I only asked you to remove R. And if R is 30 then angle sum property
87:26 And if R is 30 then angle sum property This will automatically become 60. Balance
87:29 This will automatically become 60. Balance I have also taught you this from trigonometry.
87:31 I have also taught you this from trigonometry. I had taken it out and shown it. So this way you
87:34 I had taken it out and shown it. So this way you You can do it. R your 30, P your 60, R your
87:37 You can do it. R your 30, P your 60, R your 30, P your 60. Understand the point that
87:40 30, P your 60. Understand the point that In trigonometry, you can find a triangle with a right angle.
87:43 In trigonometry, you can find a triangle with a right angle. Finding the Angles and Sides of a Triangle
87:47 Finding the Angles and Sides of a Triangle You can. Ok? I want to explain it to you further
87:50 You can. Ok? I want to explain it to you further I will try this a little. to wait
87:52 I will try this a little. to wait Patience. Listen and believe. I asked you a question
87:55 Patience. Listen and believe. I asked you a question Gave. I told you I have a right
87:57 Gave. I told you I have a right Angle is triangle. Ok? I to you
87:59 Angle is triangle. Ok? I to you Said this is 90. I told you this is 60.
88:02 Said this is 90. I told you this is 60. I told you this is A, this is B, this is C
88:05 I told you this is A, this is B, this is C Is. I am telling you that this is too diya
88:07 Is. I am telling you that this is too diya It has happened. What did I say? I told you
88:10 It has happened. What did I say? I told you That this is a given. tell me what is this
88:12 That this is a given. tell me what is this will be? Very basic thing. very basic
88:15 will be? Very basic thing. very basic talk. We have to find the side of the triangle.
88:18 talk. We have to find the side of the triangle. We have to find the side of the triangle. one thing at least
88:21 We have to find the side of the triangle. one thing at least The Pythagorean Theorem comes to mind. Second
88:23 The Pythagorean Theorem comes to mind. Second The thing that comes to mind is trigonometry.
88:25 The thing that comes to mind is trigonometry. Because it is a right angle triangle. Now I just
88:28 Because it is a right angle triangle. Now I just Tell me, if I tell you that this one
88:31 Tell me, if I tell you that this one side this side this side take out
88:33 side this side this side take out Is. Just tell me the angle you gave.
88:36 Is. Just tell me the angle you gave. What would this and this and this be for the angle?
88:40 What would this and this and this be for the angle? Think about it. For this angle, this
88:42 Think about it. For this angle, this perpendicular
88:43 perpendicular Which is this base perpendicular and base one
88:47 Which is this base perpendicular and base one What is a trigonometric ratio? tan or
88:49 What is a trigonometric ratio? tan or Then cot so can I say that
88:52 Then cot so can I say that tan 60 equi perpendicular up base
88:58 tan 60 equi perpendicular up base tan 60 = how much is perpendicular? to base
89:02 tan 60 = how much is perpendicular? to base How much? What is BC tan 60? 3 2 / BC
89:08 How much? What is BC tan 60? 3 2 / BC So what is the value of BC? Your BC has arrived
89:10 So what is the value of BC? Your BC has arrived 2 / 3 You understand what I am trying to say.
89:14 2 / 3 You understand what I am trying to say. You understand what I am trying to say. Correct
89:16 You understand what I am trying to say. Correct Is? Now let's ask you another question.
89:20 Is? Now let's ask you another question. Said that this is a right angle triangle. Correct
89:21 Said that this is a right angle triangle. Correct Is? Everyone listen carefully. Is PQR correct?
89:25 Is? Everyone listen carefully. Is PQR correct? Ok? As if I told you this angle
89:28 Ok? As if I told you this angle I have given you the angle of 45. I
89:32 I have given you the angle of 45. I I am telling you this is 45. I am telling you
89:34 I am telling you this is 45. I am telling you I am saying that this is five. tell me this
89:36 I am saying that this is five. tell me this What will happen? Tell me what will happen? So
89:39 What will happen? Tell me what will happen? So It is very easy. It is very easy. How? this angle
89:42 It is very easy. It is very easy. How? this angle This hypo is given for. this angle
89:46 This hypo is given for. this angle These perpendiculars for hypo perpendicular
89:49 These perpendiculars for hypo perpendicular Or which ratio is perpendicular hypoge
89:51 Or which ratio is perpendicular hypoge It happens? sin theta or cosec theta. So
89:54 It happens? sin theta or cosec theta. So What did you do? can I say that
89:56 What did you do? can I say that that sin 45° or let's say sin p sin of angle
90:01 that sin 45° or let's say sin p sin of angle P What will happen? What is the sin of angle P
90:04 P What will happen? What is the sin of angle P Will you go? Perpendicular Upon Hypo Angle P
90:07 Will you go? Perpendicular Upon Hypo Angle P How much is it? 45 then sin 45 perpendicular is how much
90:10 How much is it? 45 then sin 45 perpendicular is how much qr hypo is how much pr sin 45 1/2
90:17 qr hypo is how much pr sin 45 1/2 I don't know how much QR is, how much PR is five.
90:22 I don't know how much QR is, how much PR is five. See how much your QR has come
90:24 See how much your QR has come How much did your qr come to? 5 above 5/2 came to this.
90:29 How much did your qr come to? 5 above 5/2 came to this. How can you apply trigonometry?
90:31 How can you apply trigonometry? Sides and Angles in a Right Angle Triangle
90:33 Sides and Angles in a Right Angle Triangle To find out the fact, you can also find out this
90:37 To find out the fact, you can also find out this Could have. Ok? Think about it and tell me
90:42 Could have. Ok? Think about it and tell me Which ratio should you use? if these
90:44 Which ratio should you use? if these If it had to be removed, it would have been as if a hypo had been given.
90:47 If it had to be removed, it would have been as if a hypo had been given. Did not give. I have given hypo, this is not given.
90:50 Did not give. I have given hypo, this is not given. So which ratio should you use? For 45°,
90:53 So which ratio should you use? For 45°, If there is a base, then base and hypo, base and hypo you
90:55 If there is a base, then base and hypo, base and hypo you We would have used the cos ratio. cos theta.
91:00 We would have used the cos ratio. cos theta. Easy. This is how your trigonometry works.
91:03 Easy. This is how your trigonometry works. Does. Based on this, a CBSE
91:07 Does. Based on this, a CBSE It was a very nice question. Just pay attention
91:09 It was a very nice question. Just pay attention Please give it. What are you saying? The Road AC
91:11 Please give it. What are you saying? The Road AC Listen comfortably. The Road Ace of a TV
91:14 Listen comfortably. The Road Ace of a TV Disc. Ok? Take yourself to good levels
91:17 Disc. Ok? Take yourself to good levels I have to practice the question. Because
91:19 I have to practice the question. Because CBSE is now making good level papers
91:21 CBSE is now making good level papers Is. Remember this. Ok? you tension
91:23 Is. Remember this. Ok? you tension Don't take it. Just be patient. If you're a little tired
91:26 Don't take it. Just be patient. If you're a little tired Take a break. Ok? Good levels of bars
91:28 Take a break. Ok? Good levels of bars I have to practice it. Ok? Good.
91:31 I have to practice it. Ok? Good. Well, a lot of kids ask me that.
91:34 Well, a lot of kids ask me that. How can we ask questions separately?
91:35 How can we ask questions separately? Are? You should be the first priority
91:37 Are? You should be the first priority You need what I'm getting you here
91:39 You need what I'm getting you here I am there. Do these many questions well first.
91:41 I am there. Do these many questions well first. Take. After that, if you have an obvious thing
91:43 Take. After that, if you have an obvious thing Real confidence in oneself comes when
91:45 Real confidence in oneself comes when You practice on your own. So the question
91:46 You practice on your own. So the question I will put the bank link below. that question
91:49 I will put the bank link below. that question You guys have a lot of questions even after taking the bank.
91:51 You guys have a lot of questions even after taking the bank. You can practice this. that question
91:53 You can practice this. that question There are a lot of case based questions in the bank.
91:55 There are a lot of case based questions in the bank. Are. Lots of MCQ questions, lots of
91:58 Are. Lots of MCQ questions, lots of Short Answer, Long Answer, Assertion Reason
92:00 Short Answer, Long Answer, Assertion Reason There are questions. very good question
92:02 There are questions. very good question There is a bank. I will put the link below. you to me
92:04 There is a bank. I will put the link below. you to me You can practice the questions. Link
92:06 You can practice the questions. Link You will get it. Where to get it, what
92:08 You will get it. Where to get it, what Have to take it. Anyway coming to the point. [ __ ]
92:11 Have to take it. Anyway coming to the point. [ __ ] To the point. The Road AC of a TB disc
92:13 To the point. The Road AC of a TB disc The antenna is fixed at right angles to the
92:15 The antenna is fixed at right angles to the Ball AB. Good road AC road AB. something good
92:18 Ball AB. Good road AC road AB. something good You are saying something like this, I understand something
92:20 You are saying something like this, I understand something Key Road AC Road AB Road AC Road AB Road AC
92:25 Key Road AC Road AB Road AC Road AB Road AC Road AB Okay, okay. fix both
92:28 Road AB Okay, okay. fix both given at right angle means basically this gives you
92:30 given at right angle means basically this gives you 90 is given. I am trying to understand the question now
92:32 90 is given. I am trying to understand the question now I am trying to. Ok? what do you say now
92:34 I am trying to. Ok? what do you say now Used to be?
92:36 Used to be? A AC 1.5 Good AC
92:40 A AC 1.5 Good AC One side of a right angle triangle gives you 1.5
92:43 One side of a right angle triangle gives you 1.5 It is given. CD 3 is a good CD
92:47 It is given. CD 3 is a good CD CD3 is given. Okay, I gave you three.
92:51 CD3 is given. Okay, I gave you three. It has happened. Ok? Find tan theta. Good
92:55 It has happened. Ok? Find tan theta. Good You are asking me to find tan theta. Ok?
92:57 You are asking me to find tan theta. Ok? So everyone should understand one thing.
92:59 So everyone should understand one thing. Is that the thing that boss right angle
93:02 Is that the thing that boss right angle triangle right angle triangle right angle
93:04 triangle right angle triangle right angle Trigonometry can be applied to a triangle.
93:07 Trigonometry can be applied to a triangle. Is. Ok? So why not write it first?
93:10 Is. Ok? So why not write it first? Angle Triangle in Right Angle Triangle
93:13 Angle Triangle in Right Angle Triangle One side is given, the second is given and the third is removed.
93:15 One side is given, the second is given and the third is removed. I will take it. Should I do this first? Ok?
93:18 I will take it. Should I do this first? Ok? Let's go brother with Pythagoras theorem
93:22 Let's go brother with Pythagoras theorem in triangle ACD
93:25 in triangle ACD in triangle ACD
93:28 in triangle ACD Pythagoras Theorem by Pythagoras
93:31 Pythagoras Theorem by Pythagoras The theorem you should understand is that the CD
93:34 The theorem you should understand is that the CD Square will be equal to AD² + AC².
93:41 Square will be equal to AD² + AC². Ok? How much is a CD? CD is three so 3²
93:45 Ok? How much is a CD? CD is three so 3² will equal AD² AD you don't know. AC²
93:50 will equal AD² AD you don't know. AC² That means if it is 1.5 then I will write it as 15/10.
93:53 That means if it is 1.5 then I will write it as 15/10. And I am afraid of decimals, brother.
93:56 And I am afraid of decimals, brother. 3² 9 is your AD² brother, this is your 5 * 3 = 5 *
94:01 3² 9 is your AD² brother, this is your 5 * 3 = 5 * 2 then 3² 9 2² 4 so AD² what is it? AD² aa
94:07 2 then 3² 9 2² 4 so AD² what is it? AD² aa Gaya 9 - 9 / 4 Plant a forest under it. 9 / 4
94:11 Gaya 9 - 9 / 4 Plant a forest under it. 9 / 4 Here -9/4 so your LCM will be four. Correct
94:16 Here -9/4 so your LCM will be four. Correct Is? What should I multiply in one? 4 came 4
94:19 Is? What should I multiply in one? 4 came 4 So 4 * 9 36 - 9 / 4 = AD²
94:25 So 4 * 9 36 - 9 / 4 = AD² Ok? So this is your 27
94:29 Ok? So this is your 27 / 4 = AD² so square is here square
94:34 / 4 = AD² so square is here square come here plus minus
94:37 come here plus minus 27 / 4 AD is a length so it can never be negative
94:40 27 / 4 AD is a length so it can never be negative It will not happen. So the final value of AD is
94:45 It will not happen. So the final value of AD is 27 /
94:48 27 / 4 now
94:50 4 now What is 27? Look 27
94:53 What is 27? Look 27 On the 27th you
94:55 On the 27th you You can write 3 * 3 * 3. A three comes out
94:59 You can write 3 * 3 * 3. A three comes out Will go. So this is your 3 3/2 because
95:04 Will go. So this is your 3 3/2 because 4 is 2. Ok? So your AD has arrived.
95:08 4 is 2. Ok? So your AD has arrived. Find the sum of all three sides of a right angle triangle.
95:10 Find the sum of all three sides of a right angle triangle. Went. The three sides of a right-angled triangle
95:12 Went. The three sides of a right-angled triangle Got it. Now watch it comfortably. Ok? tan
95:15 Got it. Now watch it comfortably. Ok? tan We have to find theta. So tan theta does the same here
95:18 We have to find theta. So tan theta does the same here Am. The first one.
95:20 Am. The first one. What is tanθ? Perpendicular up base.
95:25 What is tanθ? Perpendicular up base. for this one theta for this one angle
95:27 for this one theta for this one angle Perpendicular and base for this angle
95:31 Perpendicular and base for this angle Tell me. This will be the base for this angle.
95:35 Tell me. This will be the base for this angle. This will be perpendicular. Think about it. this is
95:38 This will be perpendicular. Think about it. this is It's a hypo, isn't it, brother? This is hypo
95:41 It's a hypo, isn't it, brother? This is hypo This base is perpendicular. So this angle
95:45 This base is perpendicular. So this angle Pay attention to. pay attention. then tan
95:48 Pay attention to. pay attention. then tan theta
95:50 theta What is perpendicular? AC.
95:54 What is perpendicular? AC. What is the base? What is the base? AD. How much is AC? AC
95:59 What is the base? What is the base? AD. How much is AC? AC How much is it? 1.5
96:01 How much is it? 1.5 How much is AC? 1.5
96:04 How much is AC? 1.5 How much is AD? 3 3/2
96:08 How much is AD? 3 3/2 This is feeling strange, friend. That is why he speaks
96:11 This is feeling strange, friend. That is why he speaks I am telling you to do it slowly. Look how I
96:13 I am telling you to do it slowly. Look how I I will do it. Ok? Look here. so tan theta AC
96:17 I will do it. Ok? Look here. so tan theta AC How much is it? 1.5, so no problem he gets 15/
96:20 How much is it? 1.5, so no problem he gets 15/ I will write 10. divided by AD is how much
96:22 I will write 10. divided by AD is how much Is? How much is AD? Just removed it. 3 3 / 2. Now
96:26 Is? How much is AD? Just removed it. 3 3 / 2. Now You all know very well that this is the most
96:29 You all know very well that this is the most So here you go 15 * 2 / 10 * 3
96:37 So here you go 15 * 2 / 10 * 3 Do some fighting. So 2 * 1 2 * 5 * 1 5 * 3
96:43 Do some fighting. So 2 * 1 2 * 5 * 1 5 * 3 * 1 3 * 1 So this is your 1/3. tan
96:48 * 1 3 * 1 So this is your 1/3. tan theta is your 1/3 and you get tan theta
96:52 theta is your 1/3 and you get tan theta I was asked to take it out. Similarly, now you
96:54 I was asked to take it out. Similarly, now you said sec theta + cosec theta. So seconds
96:56 said sec theta + cosec theta. So seconds In the question you have been told that sec theta +
97:01 In the question you have been told that sec theta + Let's say cosec theta. what is sec theta
97:03 Let's say cosec theta. what is sec theta Is? Hypotension/Base. cosec theta what
97:07 Is? Hypotension/Base. cosec theta what It happens? Hypotensive/Perpendicular Keep
97:10 It happens? Hypotensive/Perpendicular Keep All the values. So how much is a hypo? Hypo
97:13 All the values. So how much is a hypo? Hypo How much? How much is a hypo? hypo to theta
97:16 How much? How much is a hypo? hypo to theta How much is it? Three. How much is a hypo? Three. So
97:19 How much is it? Three. How much is a hypo? Three. So This is also three. This is also three. Base perpendicular.
97:24 This is also three. This is also three. Base perpendicular. How much is base for theta to theta?
97:26 How much is base for theta to theta? AD. How much is the base? AD. AD means 3 3 / 2 AD
97:32 AD. How much is the base? AD. AD means 3 3 / 2 AD Meaning
97:34 Meaning 3 3 / 2 Please pay attention.
97:37 3 3 / 2 Please pay attention. Ok? How much is perpendicular?
97:39 Ok? How much is perpendicular? 1.5 for perpendicular theta so this is your
97:42 1.5 for perpendicular theta so this is your 1.5 means 15/10
97:46 1.5 means 15/10 What did you understand? Confused once again
97:49 What did you understand? Confused once again It should not happen. Three, hypo instead of hypo
97:52 It should not happen. Three, hypo instead of hypo Three instead of. This instead of a base, perpendicular
97:54 Three instead of. This instead of a base, perpendicular You can see this instead of all this here.
97:57 You can see this instead of all this here. I know the value. This base, this hypo, this
98:01 I know the value. This base, this hypo, this perpendicular, this base, this hypo, this
98:04 perpendicular, this base, this hypo, this Perpendicular, Perpendicular 1 5 Hypotenuse
98:07 Perpendicular, Perpendicular 1 5 Hypotenuse The base is now 3 3/2, so you just have to solve it.
98:11 The base is now 3 3/2, so you just have to solve it. Have to do it. Yes, let's. so so so so this
98:15 Have to do it. Yes, let's. so so so so this Yours has arrived. Well, if there is confusion
98:18 Yours has arrived. Well, if there is confusion What to do? Put one under three
98:20 What to do? Put one under three divided by 3 3/2 plus one under three
98:24 divided by 3 3/2 plus one under three Divide by 15/10 like this. Now
98:27 Divide by 15/10 like this. Now There is no confusion in this, boss.
98:29 There is no confusion in this, boss. Why? Because it goes up. these like these
98:32 Why? Because it goes up. these like these Will go up. This is how they solve it. So 2 *
98:36 Will go up. This is how they solve it. So 2 * 3 6 3 3 * 1 3 3 + 10 * 3 30 15 * 1 15
98:44 3 6 3 3 * 1 3 3 + 10 * 3 30 15 * 1 15 Ok? 3 * 1 = 3 * 2 so this is your 2
98:48 Ok? 3 * 1 = 3 * 2 so this is your 2 / 3 + 30 and 15, that's your 2 / 1
98:54 / 3 + 30 and 15, that's your 2 / 1 If you want to find the LCM, then the LCM of 3 and one is 3.
98:58 If you want to find the LCM, then the LCM of 3 and one is 3. 3 3 So what in up to as it is one
99:01 3 3 So what in up to as it is one Multiply it by 3 or 3 and your score will come up.
99:04 Multiply it by 3 or 3 and your score will come up. 2 3 So your final has arrived right here.
99:07 2 3 So your final has arrived right here. You can leave it or do this to common
99:09 You can leave it or do this to common Subtract 1 + 3
99:14 Subtract 1 + 3 Take out a second second to common. 1 + 3 /
99:20 Take out a second second to common. 1 + 3 / 3 This is your sec theta + cosec theta
99:23 3 This is your sec theta + cosec theta Value. If asked to keep the value of 3
99:26 Value. If asked to keep the value of 3 So keep it. Otherwise, you can leave your answer here.
99:30 So keep it. Otherwise, you can leave your answer here. You can. Well, what is the important thing?
99:31 You can. Well, what is the important thing? Meters. Meters.
99:35 Meters. Meters. Okay, right? This is coming in meters, right?
99:37 Okay, right? This is coming in meters, right? Perhaps. Okay, right?
99:40 Perhaps. Okay, right? Ok. Not good. Why meters? this is
99:42 Ok. Not good. Why meters? this is Isn't it a ratio? Ok? any unit of ratio
99:45 Isn't it a ratio? Ok? any unit of ratio It doesn't happen. Is it clear? Did you understand? So
99:48 It doesn't happen. Is it clear? Did you understand? So Your value of sec theta + cosec theta
99:51 Your value of sec theta + cosec theta It has come. Ok? Come on friend, let's move ahead. Ahead
99:56 It has come. Ok? Come on friend, let's move ahead. Ahead Let's go boss. This one too, I think
99:57 Let's go boss. This one too, I think Will be done. This will also happen. Let's go, this one
99:59 Will be done. This will also happen. Let's go, this one We do. Very nice question. very much
100:01 We do. Very nice question. very much Lovely question. What are you saying? sin theta -
100:03 Lovely question. What are you saying? sin theta - cos theta. The value of sin theta - cos theta
100:07 cos theta. The value of sin theta - cos theta It is zero. Find the value of sin to the power of 4
100:10 It is zero. Find the value of sin to the power of 4 theta + cos sin cos to the power 4 theta. These
100:13 theta + cos sin cos to the power 4 theta. These cos it is friend. There is a printing mistake here
100:15 cos it is friend. There is a printing mistake here Pay. This is cos to the power 4 theta. How is this
100:19 Pay. This is cos to the power 4 theta. How is this What to do? sin theta - cos theta 0 is given.
100:22 What to do? sin theta - cos theta 0 is given. Listen to me calmly. If given to you
100:25 Listen to me calmly. If given to you is sin theta - cos theta = 0. Ok? Two
100:30 is sin theta - cos theta = 0. Ok? Two There are ways to do this question. Now he
100:32 There are ways to do this question. Now he What are the two ways that come to your mind?
100:33 What are the two ways that come to your mind? Must have been. One way is that friend sin theta
100:36 Must have been. One way is that friend sin theta Meaning perpendicular/hypotenous. cos theta
100:39 Meaning perpendicular/hypotenous. cos theta Meaning base/hypotenuse. So if
100:42 Meaning base/hypotenuse. So if Perpendicular, base and hypotenuse i.e.
100:45 Perpendicular, base and hypotenuse i.e. Find all three sides of a right-angled triangle
100:46 Find all three sides of a right-angled triangle let's go
100:48 let's go So I can solve it by keeping it here.
100:52 So I can solve it by keeping it here. But the edge of the right angle triangle is here
100:54 But the edge of the right angle triangle is here If the truth is that nothing like this is being said then
100:56 If the truth is that nothing like this is being said then I am not able to understand anything. Second
100:59 I am not able to understand anything. Second Method if you know theta. if you
101:03 Method if you know theta. if you If we find theta, that is, if we find the angle
101:06 If we find theta, that is, if we find the angle Maybe it will work. Pay attention here now. So
101:10 Maybe it will work. Pay attention here now. So I can write sin theta = cos theta. - cos
101:15 I can write sin theta = cos theta. - cos Theta went over there so cos theta yes or no? So
101:17 Theta went over there so cos theta yes or no? So There you have it: sin theta * 1 cos theta * 1
101:21 There you have it: sin theta * 1 cos theta * 1 Is there any problem or benefit in this? sin theta
101:25 Is there any problem or benefit in this? sin theta down cos theta and these ones.
101:29 down cos theta and these ones. What is sin theta / cos theta? tan
101:32 What is sin theta / cos theta? tan Theta and these one. At what angle is tan
101:35 Theta and these one. At what angle is tan It happens? tan one at what angle? tan 45
101:39 It happens? tan one at what angle? tan 45 But then theta becomes 45 and if theta becomes 45
101:44 But then theta becomes 45 and if theta becomes 45 So basically you were asked to find the power of sin 45°
101:49 So basically you were asked to find the power of sin 45° + cos to the power of 45°
101:52 + cos to the power of 45° What is sin 45? cos 4 to the power of 1/2
101:56 What is sin 45? cos 4 to the power of 1/2 What is 45? 1/2 to the power of 4 so 1 is 4
102:01 What is 45? 1/2 to the power of 4 so 1 is 4 1 2 to the power of 4 2 to the power of 4 if not known
102:05 1 2 to the power of 4 2 to the power of 4 if not known So 2 to the power of 4 means 2 * 2 * 2 * 2 2 * 2
102:10 So 2 to the power of 4 means 2 * 2 * 2 * 2 2 * 2 2 2 * 2 2 * 2 4 2 to the power is 4
102:16 2 2 * 2 2 * 2 4 2 to the power is 4 Also your 1/4 so this is your 2/4 vs 1/
102:20 Also your 1/4 so this is your 2/4 vs 1/ 2 So here is your answer, 1/2
102:23 2 So here is your answer, 1/2 What did I do? I took out theta.
102:27 What did I do? I took out theta. Once you find theta, you will get the answer. Ok?
102:30 Once you find theta, you will get the answer. Ok? How to find theta? This was a given. As such
102:32 How to find theta? This was a given. As such Get cos theta down to sin theta / cos theta
102:36 Get cos theta down to sin theta / cos theta 1 sin theta / cos theta one sin theta / cos
102:38 1 sin theta / cos theta one sin theta / cos At what angle is theta tan theta tan one
102:41 At what angle is theta tan theta tan one Is? So theta at 45 is your 45.
102:44 Is? So theta at 45 is your 45. This way you should get questions about ratios.
102:47 This way you should get questions about ratios. For some specific angles. Ok? One
102:51 For some specific angles. Ok? One Let's see half more and then we will move ahead. Let us go
102:53 Let's see half more and then we will move ahead. Let us go Let's move on to the next one. very cute
102:55 Let's move on to the next one. very cute Question. What about this angle concept?
102:58 Question. What about this angle concept? Are you speaking? If theta is an acute angle.
103:00 Are you speaking? If theta is an acute angle. You have to read it very comfortably. to the question
103:02 You have to read it very comfortably. to the question Have to try to understand. as much as you can
103:04 Have to try to understand. as much as you can We have to try to do as much as we can. Ok?
103:06 We have to try to do as much as we can. Ok? So theta is what you're told is the acute angle.
103:08 So theta is what you're told is the acute angle. Meaning theta is any angle less than 90°
103:11 Meaning theta is any angle less than 90° will be. Ok? of tan theta + cot theta
103:14 will be. Ok? of tan theta + cot theta Value to is given. Ok? tan of someone
103:17 Value to is given. Ok? tan of someone angle theta, cot of any angle theta plus
103:20 angle theta, cot of any angle theta plus Karke 2 is coming. Find the value of tan
103:22 Karke 2 is coming. Find the value of tan to the power of 7 theta + cot to the power of 7 theta. Brother
103:26 to the power of 7 theta + cot to the power of 7 theta. Brother Sir, hashtag QD is the question, right? QD
103:30 Sir, hashtag QD is the question, right? QD This is a very lovely question. Now friend
103:33 This is a very lovely question. Now friend How to do this query? if you look
103:35 How to do this query? if you look Fatally, friend, this power consumption is very dangerous.
103:38 Fatally, friend, this power consumption is very dangerous. There is sea power. Meaning if it is square,
103:41 There is sea power. Meaning if it is square, Even if it were a cube, I would still have a little
103:42 Even if it were a cube, I would still have a little I understand. I feel comfortable
103:44 I understand. I feel comfortable Am. How do I do this from power to power 100? Now
103:48 Am. How do I do this from power to power 100? Now Well by the way, instead of power seven, here
103:51 Well by the way, instead of power seven, here Power 100 Power 500 could also have been written. So
103:54 Power 100 Power 500 could also have been written. So How to do it? one thing is if theta
103:57 How to do it? one thing is if theta If I get to know the value then it will be good for me.
104:00 If I get to know the value then it will be good for me. The question may be simple. Because if theta
104:02 The question may be simple. Because if theta Suppose it is 30° then put the value of tan 30°
104:05 Suppose it is 30° then put the value of tan 30° Give. I will increase its power to 7. means one
104:08 Give. I will increase its power to 7. means one The way is that I should find out theta. But
104:11 The way is that I should find out theta. But Pay attention to find theta. I
104:13 Pay attention to find theta. I If you want, I can tell you directly. But
104:15 If you want, I can tell you directly. But I'm making you think. If you
104:17 I'm making you think. If you If you can catch it, if you can understand it. Ok? So now
104:21 If you can catch it, if you can understand it. Ok? So now How do I find out theta? theta me then
104:24 How do I find out theta? theta me then You will find out when you do a trigonometric test here.
104:26 You will find out when you do a trigonometric test here. The ratio will be on one side. that's what you're doing
104:30 The ratio will be on one side. that's what you're doing Since is a trigonometric ratio.
104:32 Since is a trigonometric ratio. Then compare the values and find the value of the angle.
104:34 Then compare the values and find the value of the angle. We are finding out. Isn't it? The second way is that
104:38 We are finding out. Isn't it? The second way is that I need to find the value of tan theta i.e. perpendicular
104:40 I need to find the value of tan theta i.e. perpendicular / Base means the same right angle triangle
104:43 / Base means the same right angle triangle Story but something like a right angle triangle
104:45 Story but something like a right angle triangle I have not kept it. So I had the same mind
104:48 I have not kept it. So I had the same mind Applied. Why don't I give this a
104:50 Applied. Why don't I give this a Convert to trigonometric ratio.
104:52 Convert to trigonometric ratio. How will I do that now? Listen carefully. Good
104:54 How will I do that now? Listen carefully. Good The question is. Look, I have been given tanθ
104:58 The question is. Look, I have been given tanθ + cot theta = 2.
105:01 + cot theta = 2. okay brother? Now this has the same
105:03 okay brother? Now this has the same I do it in trigonometric ratio. One
105:04 I do it in trigonometric ratio. One I work. I do it in tan. Now tan
105:06 I work. I do it in tan. Now tan How did I do it? listen and see
105:07 How did I do it? listen and see Pay attention to your meditation. So tan theta + cot
105:11 Pay attention to your meditation. So tan theta + cot Write theta as 1 / tan theta. can I
105:13 Write theta as 1 / tan theta. can I Can I do this? I can definitely do it.
105:15 Can I do this? I can definitely do it. tan theta cot theta reciprocal of each other
105:17 tan theta cot theta reciprocal of each other It happens. Meaning I'm dividing cot theta by 1/tan
105:20 It happens. Meaning I'm dividing cot theta by 1/tan I can write theta. Now what is the benefit of this?
105:22 I can write theta. Now what is the benefit of this? Happened? Listen, listen carefully. Ok?
105:25 Happened? Listen, listen carefully. Ok? I will take LCM. Obviously here LCM
105:27 I will take LCM. Obviously here LCM will have to take. Ok? Brother, if 1+1/2
105:30 will have to take. Ok? Brother, if 1+1/2 If it is written then you will feel like taking LCM, right?
105:32 If it is written then you will feel like taking LCM, right? So here also if I put a forest below it then
105:34 So here also if I put a forest below it then LCM of one and tan theta is not to be alarmed.
105:39 LCM of one and tan theta is not to be alarmed. The remaining lectures that follow are there
105:41 The remaining lectures that follow are there All you have to do is what I'm doing here now.
105:44 All you have to do is what I'm doing here now. I am going to do it. Ok? of one and tan theta
105:46 I am going to do it. Ok? of one and tan theta LCM tan theta. Now in the forest, now listen to the forest and
105:50 LCM tan theta. Now in the forest, now listen to the forest and LCM of tan theta tan theta. tan theta
105:53 LCM of tan theta tan theta. tan theta tan theta so up here as it is one a
105:55 tan theta so up here as it is one a Will go. because tan theta over here
105:57 Will go. because tan theta over here also tan theta. one here tan theta
105:59 also tan theta. one here tan theta So what should I multiply in one? tan theta
106:01 So what should I multiply in one? tan theta Is. What should I multiply in one? tan
106:04 Is. What should I multiply in one? tan is theta. tan theta is divided by tan theta above
106:06 is theta. tan theta is divided by tan theta above Multiply it. tanθ * tan theta is
106:10 Multiply it. tanθ * tan theta is tan² theta. Is this understanding? Equ 2 now
106:14 tan² theta. Is this understanding? Equ 2 now Tan theta will obviously go up. So
106:16 Tan theta will obviously go up. So There you have it, tan² theta + 1 = 2 tan
106:21 There you have it, tan² theta + 1 = 2 tan Theta. Ok? Now a little bit here
106:24 Theta. Ok? Now a little bit here There may be difficulties. But no problem.
106:27 There may be difficulties. But no problem. This is new for you guys but not difficult.
106:29 This is new for you guys but not difficult. Is. You will learn something good from this lecture.
106:31 Is. You will learn something good from this lecture. pay attention. Ok? Such in class 11th
106:34 pay attention. Ok? Such in class 11th Many equations will be formed. Now if you
106:36 Many equations will be formed. Now if you Can you use your brain even a little bit, what kind of equation is this?
106:39 Can you use your brain even a little bit, what kind of equation is this? Can you see it? Assume. Look, let's
106:42 Can you see it? Assume. Look, let's I if I let I x equal to or
106:45 I if I let I x equal to or Then let tan theta look up here. I
106:49 Then let tan theta look up here. I Let tanθ be x. What is the benefit of this now?
106:52 Let tanθ be x. What is the benefit of this now? will be? Hear Ok? I converted tan theta
106:55 will be? Hear Ok? I converted tan theta Let x be why? Understand. Now if I
106:58 Let x be why? Understand. Now if I Let tanθ be x, then write x in place of tan theta.
107:02 Let tanθ be x, then write x in place of tan theta. Gave. x² So this is your x². look here
107:06 Gave. x² So this is your x². look here Let -2 tan theta be x, so write x here.
107:10 Let -2 tan theta be x, so write x here. + 1 = 0 Do you understand what happened? you understood
107:13 + 1 = 0 Do you understand what happened? you understood What? A quadratic equation was formed. One
107:16 What? A quadratic equation was formed. One It became a quadratic equation. Now
107:18 It became a quadratic equation. Now Mind to solve quadratic equations
107:20 Mind to solve quadratic equations Will do. Apply middle term spatting. two such
107:22 Will do. Apply middle term spatting. two such Numbers that multiply to 1 * 1 1
107:26 Numbers that multiply to 1 * 1 1 Which when added gives the coefficient of x as -2.
107:30 Which when added gives the coefficient of x as -2. What would be two such numbers? two such
107:32 What would be two such numbers? two such Numbers you can take -1 and -1 why so?
107:36 Numbers you can take -1 and -1 why so? -1 + -1 -2 By multiplying these two
107:40 -1 + -1 -2 By multiplying these two Forest. Plus these two and then -2 is just x²
107:43 Forest. Plus these two and then -2 is just x² Substitute -2x for -1x - 1x + 1 = 0
107:49 Substitute -2x for -1x - 1x + 1 = 0 Mid-term splitting, I think.
107:51 Mid-term splitting, I think. Everyone knows it. Ok? Come on boss then x
107:54 Everyone knows it. Ok? Come on boss then x Common taken x - 1 from here -1 common taken x -
107:58 Common taken x - 1 from here -1 common taken x - You can also check if 1 = 0. -1 * x -1x -1 *
108:04 You can also check if 1 = 0. -1 * x -1x -1 * -1 +1 x - 1 x - 1 is common in both then x -
108:09 -1 +1 x - 1 x - 1 is common in both then x - So we take out 1 and we're left with x here.
108:11 So we take out 1 and we're left with x here. So, now x - 1 = 0, x - 1 = 0
108:17 So, now x - 1 = 0, x - 1 = 0 So when x - 1 = 0 and x - 1 = 0 you will get x
108:22 So when x - 1 = 0 and x - 1 = 0 you will get x Two values are coming 1 and 1 and 1
108:26 Two values are coming 1 and 1 and 1 How? See, x - 1 = 0, so the value of x
108:29 How? See, x - 1 = 0, so the value of x Forest. x - 1 = 0 so the value of x is one. Ok?
108:32 Forest. x - 1 = 0 so the value of x is one. Ok? Now x1 has arrived. Now what is the benefit of this? x1
108:35 Now x1 has arrived. Now what is the benefit of this? x1 I have arrived. What did tan brother x mean? tan theta.
108:39 I have arrived. What did tan brother x mean? tan theta. What is x? tan theta. This means to say
108:43 What is x? tan theta. This means to say Implies that tan theta has the value of one.
108:46 Implies that tan theta has the value of one. Now at what angle does tan equal one? tan
108:50 Now at what angle does tan equal one? tan At which angle is the forest? at tan 45°.
108:54 At which angle is the forest? at tan 45°. So instead of one, 45° was written. And here brother on
108:58 So instead of one, 45° was written. And here brother on Comparison
109:00 Comparison Theta is 45°
109:03 Theta is 45° Theta is 45°
109:06 Theta is 45° Okay, and theta is 45°, so there's tan.
109:10 Okay, and theta is 45°, so there's tan. Key Power 7 45° +
109:15 Key Power 7 45° + What is 7 to the cot power equal to 45°? tan 45
109:20 What is 7 to the cot power equal to 45°? tan 45 1 to the power of 7 cot 45 1 to the power of 7 1 to the power
109:25 1 to the power of 7 cot 45 1 to the power of 7 1 to the power Do anything, one then it comes to that is
109:29 Do anything, one then it comes to that is Your Answer
109:31 Your Answer Understand how I found the angle, Bhaijaan.
109:34 Understand how I found the angle, Bhaijaan. It's clear to everyone that brother, if I knew the angle
109:36 It's clear to everyone that brother, if I knew the angle I have a trigonometric
109:39 I have a trigonometric The ratio should be one per side
109:41 The ratio should be one per side Trigonometric ratios come to one side
109:44 Trigonometric ratios come to one side How did you make him do this, what did you do with it
109:47 How did you make him do this, what did you do with it convert it to theta little by little
109:48 convert it to theta little by little Get it solved. a quadratic coming here
109:51 Get it solved. a quadratic coming here A type of equation is being formed. where x
109:53 A type of equation is being formed. where x The value is tan theta. So if you take out x
109:56 The value is tan theta. So if you take out x Meaning tan theta will come up. that was a nice question
109:59 Meaning tan theta will come up. that was a nice question Do this separately. Ok? and such
110:03 Do this separately. Ok? and such What questions may arise? absolutely come
110:05 What questions may arise? absolutely come Can. Especially those with standard maths
110:07 Can. Especially those with standard maths To. Ok? So here's your Major Major.
110:10 To. Ok? So here's your Major Major. The whole part is over. means two
110:12 The whole part is over. means two Things end. Asking another question
110:14 Things end. Asking another question Are. A very nice question of assertion reason.
110:16 Are. A very nice question of assertion reason. Khar asarshan region is known to everyone. How
110:18 Khar asarshan region is known to everyone. How There are questions. I by questioning
110:19 There are questions. I by questioning I will show you. This is a very simple question.
110:21 I will show you. This is a very simple question. What are you saying? Good By The Way Assertion
110:23 What are you saying? Good By The Way Assertion In the region, you are basically given two statements.
110:25 In the region, you are basically given two statements. There are. Gave two statements. These you
110:27 There are. Gave two statements. These you Check whether both these statements are correct or not.
110:29 Check whether both these statements are correct or not. It is wrong. All I have to do is check it out
110:31 It is wrong. All I have to do is check it out Is. Let's start with statement number one.
110:34 Is. Let's start with statement number one. Statement No. A which he asserted
110:37 Statement No. A which he asserted I have said it. Ok? ABCD is a
110:41 I have said it. Ok? ABCD is a Rectangle. pay attention. 1 second 1 second.
110:44 Rectangle. pay attention. 1 second 1 second. Yes. Ok?
110:46 Yes. Ok? So ABCD is a rectangle so that angle CAB =
110:52 So ABCD is a rectangle so that angle CAB = 60° then one thing is understood that a
110:54 60° then one thing is understood that a It is a rectangle. Ok? There is a rectangle.
110:57 It is a rectangle. Ok? There is a rectangle. Do as much as you can. This thing I
111:00 Do as much as you can. This thing I I am saying this again and again. ABCD rectangle is true
111:03 I am saying this again and again. ABCD rectangle is true That C AB CAB talking about good CAB
111:08 That C AB CAB talking about good CAB Are. CAB will have to be joined by CA. CAB
111:12 Are. CAB will have to be joined by CA. CAB You are being given 60°. very nice. AC
111:16 You are being given 60°. very nice. AC You are being given A units. So, the AC
111:18 You are being given A units. So, the AC The value you are being given is A. the area of
111:21 The value you are being given is A. the area of Rectangle ABCD is 3/2a² units. To you
111:25 Rectangle ABCD is 3/2a² units. To you What are you saying about the area of the rectangle?
111:28 What are you saying about the area of the rectangle? will come to 3/2a²
111:31 will come to 3/2a² Units.
111:32 Units. Brother. Now how will the area of the rectangle be found?
111:36 Brother. Now how will the area of the rectangle be found? The formula for the area of a rectangle is
111:40 The formula for the area of a rectangle is Length * Breadth. But I don't know the length, nor
111:43 Length * Breadth. But I don't know the length, nor I know the breadth, but I don't know the length,
111:45 I know the breadth, but I don't know the length, I know the breadth, but I don't know the length,
111:47 I know the breadth, but I don't know the length, I know the breadth. But no problem. Length and
111:49 I know the breadth. But no problem. Length and Breadth can be removed. How? These 90
111:52 Breadth can be removed. How? These 90 It happens big. This is 90, big. yes friend
111:56 It happens big. This is 90, big. yes friend This is 90. Ok? So do you
111:58 This is 90. Ok? So do you Do you see this right angle triangle? This right angle
112:01 Do you see this right angle triangle? This right angle Everyone will focus in the triangle. This
112:04 Everyone will focus in the triangle. This I will make it separately for you. these ones
112:07 I will make it separately for you. these ones In triangle ABC, it's 90.
112:10 In triangle ABC, it's 90. This is given to you. It gave you 60
112:13 This is given to you. It gave you 60 It has happened. Now what is trigonometry?
112:14 It has happened. Now what is trigonometry? Trigonometry in Right Angle Triangle
112:15 Trigonometry in Right Angle Triangle Can be installed to remove sides and angles
112:18 Can be installed to remove sides and angles For. Now you tell me 60° for 60°
112:22 For. Now you tell me 60° for 60° This has become hypo for me. Ye Base Ye
112:26 This has become hypo for me. Ye Base Ye perpendicular
112:28 perpendicular These hypos.
112:30 These hypos. You have to find the base and perpendicular.
112:32 You have to find the base and perpendicular. Why? Brother, if you find out the base,
112:35 Why? Brother, if you find out the base, If you find out the perpendicular, then the rectangle
112:37 If you find out the perpendicular, then the rectangle Length and breadth will come. Area Extract
112:40 Length and breadth will come. Area Extract You can. Are you able to understand this? So
112:42 You can. Are you able to understand this? So What is the rough estimate? This base for 60°
112:44 What is the rough estimate? This base for 60° Hypo This is a perpendicular hypo given.
112:47 Hypo This is a perpendicular hypo given. Hypo is given. Base and Perpendicular
112:49 Hypo is given. Base and Perpendicular Have to take it out. So which trigonometric
112:51 Have to take it out. So which trigonometric Missing the ratio? For example, if
112:53 Missing the ratio? For example, if Hypo is given. The base has to be removed. Hypo
112:55 Hypo is given. The base has to be removed. Hypo Has given. The base has to be removed. Hypo is given.
112:57 Has given. The base has to be removed. Hypo is given. The base has to be removed. Which one is with B and H?
112:59 The base has to be removed. Which one is with B and H? What is a trigonometric ratio? cos or else
113:01 What is a trigonometric ratio? cos or else Sec. Let me do something cos 60 cos 60
113:05 Sec. Let me do something cos 60 cos 60 What happens? Base/Hypotenuse
113:08 What happens? Base/Hypotenuse Now what is the value of cos 60? cos 60
113:11 Now what is the value of cos 60? cos 60 Yours is 1/2. How much base? How much base? Base
113:15 Yours is 1/2. How much base? How much base? Base your ab hypo your a so ab come your a
113:21 your ab hypo your a so ab come your a / 2
113:22 / 2 Did you understand? Ok? Now if I have
113:26 Did you understand? Ok? Now if I have Perpendicular removal is required, hypo is given then
113:28 Perpendicular removal is required, hypo is given then P and H remind us of sin. So sin 60
113:33 P and H remind us of sin. So sin 60 = perpendicular up hypotenuse sin 60 your
113:37 = perpendicular up hypotenuse sin 60 your 3/2 Perpendicular means BC is it right? And
113:41 3/2 Perpendicular means BC is it right? And Your hypo means A, so BC is your A
113:45 Your hypo means A, so BC is your A If I went there, it would be 3/2a
113:48 If I went there, it would be 3/2a 3 / 2a
113:50 3 / 2a Easy. Ok? So AB came, BC came. AB come
113:54 Easy. Ok? So AB came, BC came. AB come Went, BC came, AB came, BC came. Area
113:57 Went, BC came, AB came, BC came. Area Off rectangle everyone will notice. Area
114:00 Off rectangle everyone will notice. Area of rectangle length * breadth. The length you
114:03 of rectangle length * breadth. The length you You can say AB.
114:06 You can say AB. You can call breadth as BC.
114:09 You can call breadth as BC. ab instead of ab / 2 instead of bc 3 /
114:16 ab instead of ab / 2 instead of bc 3 / 2a so you see a * a²
114:20 2a so you see a * a² 3a² / 4 is approaching 3a² / 4. 3a² / 2 4
114:26 3a² / 4 is approaching 3a² / 4. 3a² / 2 4 What did they give? He said that
114:27 What did they give? He said that Area of rectangle if 3a² / 2 3a² / 2
114:32 Area of rectangle if 3a² / 2 3a² / 2 We're getting 3a² / 4. He gave the wrong
114:35 We're getting 3a² / 4. He gave the wrong The area of the rectangle is given. It's coming
114:38 The area of the rectangle is given. It's coming Your area of the rectangle. with the unit
114:40 Your area of the rectangle. with the unit If you want to write this then put it at the end.
114:42 If you want to write this then put it at the end. Square units. Because Aria always
114:44 Square units. Because Aria always Square Centimeter Square Meter
114:46 Square Centimeter Square Meter It comes in square kilometers. now here
114:48 It comes in square kilometers. now here If you don't know the units, just write the units.
114:50 If you don't know the units, just write the units. Gave. This area is coming. which means that
114:53 Gave. This area is coming. which means that Your assertion is wrong. which means that assertion
114:56 Your assertion is wrong. which means that assertion That means your first statement is wrong.
115:01 That means your first statement is wrong. Is. Ok? Now let's do the second check. and
115:04 Is. Ok? Now let's do the second check. and The value of sin 60 3/2 is the value of sin 60
115:07 The value of sin 60 3/2 is the value of sin 60 How much is it? Is it 3/2?
115:09 How much is it? Is it 3/2? Absolutely. What is the value of cos 60?
115:11 Absolutely. What is the value of cos 60? 1/2 So this is given correctly. Understood
115:14 1/2 So this is given correctly. Understood Used to be? So the statement means Reese gives you the right
115:18 Used to be? So the statement means Reese gives you the right is given. Did you understand? There were two statements.
115:21 is given. Did you understand? There were two statements. One's name is Asarshan, one's name is Reese. This is wrong
115:24 One's name is Asarshan, one's name is Reese. This is wrong Is. The second one is correct.
115:28 Is. The second one is correct. Ok? So you understand it here.
115:30 Ok? So you understand it here. So which option will be correct? Assertion wrong
115:33 So which option will be correct? Assertion wrong Yes, Reese is right. Assertion is false, assertion
115:37 Yes, Reese is right. Assertion is false, assertion is false but reason R is true. Easy. clear
115:41 is false but reason R is true. Easy. clear Is? In questions with assertion reason, just this
115:43 Is? In questions with assertion reason, just this The child has to do both the statements
115:46 The child has to do both the statements Check whether it is right or wrong. and that
115:49 Check whether it is right or wrong. and that You have to answer accordingly. Ok? clear?
115:52 You have to answer accordingly. Ok? clear? Easy stuff I think. Let us go. Now finally
115:55 Easy stuff I think. Let us go. Now finally Let's move on to the third and last thing in the chapter.
115:58 Let's move on to the third and last thing in the chapter. that is and the most important thing that is
116:00 that is and the most important thing that is Trigonometric Identities.
116:03 Trigonometric Identities. Ok? I know the video is still a bit long.
116:05 Ok? I know the video is still a bit long. It has become a bit long. But it doesn't matter.
116:08 It has become a bit long. But it doesn't matter. You should go with the thought that the maths paper
116:10 You should go with the thought that the maths paper Difficult times are coming and accordingly we
116:13 Difficult times are coming and accordingly we Practice and I promise you
116:15 Practice and I promise you once again in the middle of a lecture
116:17 once again in the middle of a lecture that if you do as much as I am doing
116:19 that if you do as much as I am doing If you do it carefully, your work will be done.
116:21 If you do it carefully, your work will be done. Ok? And also very cute
116:24 Ok? And also very cute If you want to practice questions
116:26 If you want to practice questions I will tell you the book. already
116:28 I will tell you the book. already I have already told you. Go for the question bank.
116:30 I have already told you. Go for the question bank. The link to the question bank has been attached. Correct
116:32 The link to the question bank has been attached. Correct Is? The very best in this
116:33 Is? The very best in this You will get the questions. Correct
116:35 You will get the questions. Correct Is? I am putting the link. please do what
116:38 Is? I am putting the link. please do what The children want to do it. Ok? Let go,
116:41 The children want to do it. Ok? Let go, Let's move ahead with this. Let's talk.
116:44 Let's move ahead with this. Let's talk. Let's talk about the most important part of the chapter.
116:46 Let's talk about the most important part of the chapter. of the thing. that is that is trigonometric
116:50 of the thing. that is that is trigonometric Identities. Now let's recall once again
116:52 Identities. Now let's recall once again Are. We watched the next 15 minutes which
116:56 Are. We watched the next 15 minutes which Listened carefully to all the questions.
116:58 Listened carefully to all the questions. You will start becoming one. This one
117:00 You will start becoming one. This one You should have patience on this part.
117:02 You should have patience on this part. Will have to. Can you have patience? keep
117:05 Will have to. Can you have patience? keep You can definitely do it. The promise will be made. otherwise
117:07 You can definitely do it. The promise will be made. otherwise It will not be made. Listen quietly. completely on its own
117:10 It will not be made. Listen quietly. completely on its own Open it. Do that to me, to me
117:12 Open it. Do that to me, to me Two. Sacrifice it, brother, you are mine
117:14 Two. Sacrifice it, brother, you are mine At once. Okay, right? Yes. And have faith.
117:18 At once. Okay, right? Yes. And have faith. Let us go. So reciprocal identity first
117:20 Let us go. So reciprocal identity first You know that sin theta cosec theta is
117:23 You know that sin theta cosec theta is Reciprocal cos theta sec theta one of the second
117:26 Reciprocal cos theta sec theta one of the second Reciprocal tan theta cot theta one of the other
117:29 Reciprocal tan theta cot theta one of the other Reciprocal of the other question
117:31 Reciprocal of the other question What happens to tan theta in the identity
117:32 What happens to tan theta in the identity You can write sin / cos cot theta.
117:35 You can write sin / cos cot theta. You can write cos / sin now what does it mean
117:38 You can write cos / sin now what does it mean This means that if necessary
117:41 This means that if necessary Listen to me whenever you need me
117:44 Listen to me whenever you need me But it is written sin theta, then instead of that write 1 / cos
117:48 But it is written sin theta, then instead of that write 1 / cos You can write cosec theta. If it is written somewhere
117:50 You can write cosec theta. If it is written somewhere is cosec theta so instead of that we get 1 / sin theta
117:53 is cosec theta so instead of that we get 1 / sin theta You can write. Are you able to understand this?
117:55 You can write. Are you able to understand this? If it is written somewhere sin² theta then its
117:58 If it is written somewhere sin² theta then its Instead you can write 1 / cosec² theta. If
118:01 Instead you can write 1 / cosec² theta. If Somewhere it is written cosec² theta, then instead of that
118:04 Somewhere it is written cosec² theta, then instead of that You can write 1 / sin² theta. Keep listening.
118:07 You can write 1 / sin² theta. Keep listening. If it is written cos theta somewhere then instead of it
118:10 If it is written cos theta somewhere then instead of it But you can write 1 / sec theta. if somewhere
118:14 But you can write 1 / sec theta. if somewhere But it is written sec theta, so in its place you can write 1
118:17 But it is written sec theta, so in its place you can write 1 You can write / cos theta. If it is written somewhere
118:20 You can write / cos theta. If it is written somewhere is cos
118:21 is cos If theta is written somewhere as cos theta then
118:25 If theta is written somewhere as cos theta then Instead, you can write 1 / sec theta.
118:29 Instead, you can write 1 / sec theta. If it is written somewhere sec theta then instead of it
118:32 If it is written somewhere sec theta then instead of it You can write 1 / cos theta. This would mean
118:34 You can write 1 / cos theta. This would mean is the reciprocal identity. if somewhere
118:38 is the reciprocal identity. if somewhere If it is written tan² theta then instead of that you would write 1 /
118:42 If it is written tan² theta then instead of that you would write 1 / You can write cot² theta. If it is written somewhere
118:45 You can write cot² theta. If it is written somewhere is cot theta so instead you get 1 / tan theta
118:50 is cot theta so instead you get 1 / tan theta You can write. Are you able to understand this?
118:53 You can write. Are you able to understand this? If it is written tan theta somewhere then instead of it
118:55 If it is written tan theta somewhere then instead of it 1 / cot theta. Somewhere it is written cot theta
118:57 1 / cot theta. Somewhere it is written cot theta So instead of that, 1 / tan theta. Did you understand this?
119:01 So instead of that, 1 / tan theta. Did you understand this? Ok? So roughly sin cosec together
119:04 Ok? So roughly sin cosec together It works. I am a friend. cos and sec are friends.
119:07 It works. I am a friend. cos and sec are friends. Tan and Cot are friends. This thing has to be remembered.
119:10 Tan and Cot are friends. This thing has to be remembered. Ok? Ok? And one of the most important
119:13 Ok? Ok? And one of the most important You can convert sin and cosec into each other.
119:17 You can convert sin and cosec into each other. You can do it. You can convert cos and sec into each other.
119:19 You can do it. You can convert cos and sec into each other. You can change it. You can combine tan and cot into one
119:22 You can change it. You can combine tan and cot into one You can change it to another one. Keep listening.
119:24 You can change it to another one. Keep listening. Keep listening. It will be made for you. Stop. Correct
119:26 Keep listening. It will be made for you. Stop. Correct Is? What is the game of questioning identity?
119:28 Is? What is the game of questioning identity? that if it is written somewhere tan theta then its
119:31 that if it is written somewhere tan theta then its Instead you can write sin/cos. if somewhere
119:33 Instead you can write sin/cos. if somewhere If it is written cot theta then instead of that you can write cos /
119:36 If it is written cot theta then instead of that you can write cos / You can write sin. If it is written somewhere
119:38 You can write sin. If it is written somewhere tan² theta so instead you use sin² / cos²
119:42 tan² theta so instead you use sin² / cos² You can write theta. If it is written somewhere
119:43 You can write theta. If it is written somewhere cot² theta so instead you get cos² / sin²
119:48 cot² theta so instead you get cos² / sin² You can write theta. Did you understand? I
119:50 You can write theta. Did you understand? I Got the point? Now this is done. Now its
119:54 Got the point? Now this is done. Now its The last thing after that is one end
119:57 The last thing after that is one end Squared identities. into what
119:58 Squared identities. into what It happens? You just have to remember three. In this
120:01 It happens? You just have to remember three. In this Who walks with whom? number one sin² theta
120:05 Who walks with whom? number one sin² theta + I do this with white.
120:09 + I do this with white. sin² theta + cos² theta is one. This
120:14 sin² theta + cos² theta is one. This Remember this. Ok? sec² theta is 1 +
120:20 Remember this. Ok? sec² theta is 1 + tan² theta.
120:23 tan² theta. Ok? cosec²
120:26 Ok? cosec² theta is 1 + cot² theta. These three more
120:31 theta is 1 + cot² theta. These three more Remember, the work will be done. But what I say
120:34 Remember, the work will be done. But what I say Meaning of keep listening, patience. brother to me
120:37 Meaning of keep listening, patience. brother to me Tell me what this means, it means that if
120:40 Tell me what this means, it means that if Somewhere it is written sin² + cos², instead of that you
120:42 Somewhere it is written sin² + cos², instead of that you You can write direct one. If you say so
120:44 You can write direct one. If you say so I will also give you proof. Ok? if somewhere
120:47 I will also give you proof. Ok? if somewhere But it is written sin² + cos², instead of that you can write one
120:50 But it is written sin² + cos², instead of that you can write one You can write. But at the same time, brother, if now
120:53 You can write. But at the same time, brother, if now Look, right now both are here, if cos² goes there then one
120:55 Look, right now both are here, if cos² goes there then one And identity is formed. that is sin²
120:58 And identity is formed. that is sin² theta = 1 - cos² theta. Now you can put cos² there.
121:03 theta = 1 - cos² theta. Now you can put cos² there. Took it away. Now do one thing, take sin² there.
121:05 Took it away. Now do one thing, take sin² there. So cos² will remain here. cos² sin² there then
121:09 So cos² will remain here. cos² sin² there then What do you mean by saying 1 - sin²? to say
121:13 What do you mean by saying 1 - sin²? to say This means that if it is written somewhere
121:15 This means that if it is written somewhere sin² theta
121:17 sin² theta So instead of that you can write 1 - cos² theta.
121:21 So instead of that you can write 1 - cos² theta. If it is written somewhere 1 - cos² theta then
121:24 If it is written somewhere 1 - cos² theta then Instead, you can write sin² theta.
121:26 Instead, you can write sin² theta. Patience
121:28 Patience Patience, I know you have questions.
121:30 Patience, I know you have questions. You are waiting but have patience. Absolute
121:32 You are waiting but have patience. Absolute Patience. Have faith in me. the manner in which
121:34 Patience. Have faith in me. the manner in which I am teaching in a way hardly anyone
121:36 I am teaching in a way hardly anyone Teach. Have faith. Ok? Let us go. if somewhere
121:40 Teach. Have faith. Ok? Let us go. if somewhere But listen if it is written somewhere cos² theta,
121:43 But listen if it is written somewhere cos² theta, So instead of that you can write 1 - sin²
121:46 So instead of that you can write 1 - sin² Theta. If it says 1 - sin² theta,
121:49 Theta. If it says 1 - sin² theta, So instead of that you can write cos² theta.
121:52 So instead of that you can write cos² theta. How to remember so much? Oh no!
121:54 How to remember so much? Oh no! I have to remember so much. Just remember the first one
121:56 I have to remember so much. Just remember the first one Keep. that sin² + cos² goes together.
121:59 Keep. that sin² + cos² goes together. sin² + cos² is one. sin² + cos²
122:01 sin² + cos² is one. sin² + cos² There is forest. Ok? So I'm telling you guys this
122:05 There is forest. Ok? So I'm telling you guys this I have to remember this. Ok? similarly here
122:08 I have to remember this. Ok? similarly here But both things are here brother. two things
122:10 But both things are here brother. two things It's here. Bring them here one by one. So this
122:12 It's here. Bring them here one by one. So this What will become of you? sec² theta one came here
122:16 What will become of you? sec² theta one came here So - 1 = tan² theta. Bring tan² over here.
122:21 So - 1 = tan² theta. Bring tan² over here. So this becomes your sec² theta
122:24 So this becomes your sec² theta - tan² theta = 1. That is to say, to say
122:28 - tan² theta = 1. That is to say, to say This means that if it is written somewhere
122:31 This means that if it is written somewhere sec² theta, so instead you write 1 + tan² theta
122:34 sec² theta, so instead you write 1 + tan² theta Can write. If it is written somewhere 1 +
122:35 Can write. If it is written somewhere 1 + tan² theta, so instead you write sec² theta
122:38 tan² theta, so instead you write sec² theta Can. If it is written somewhere sec² theta
122:40 Can. If it is written somewhere sec² theta - 1, so instead you get tan tan² theta
122:43 - 1, so instead you get tan tan² theta You can write directly. If it is written somewhere
122:46 You can write directly. If it is written somewhere is tan² theta, so instead you replace it with sec² theta -
122:49 is tan² theta, so instead you replace it with sec² theta - You can write 1. If it is written somewhere sec²
122:52 You can write 1. If it is written somewhere sec² - tan² so you can write one instead.
122:56 - tan² so you can write one instead. Do you understand the point? Same thing here
122:58 Do you understand the point? Same thing here Both things are here. So here one by one
122:59 Both things are here. So here one by one Bring it. So it was as if he brought the forest here. So this
123:01 Bring it. So it was as if he brought the forest here. So this Yours becomes cosec² theta - 1 = cot² theta.
123:06 Yours becomes cosec² theta - 1 = cot² theta. Bring the cot² here and it's yours.
123:09 Bring the cot² here and it's yours. cosec² theta - cot² theta = 1. Ok?
123:14 cosec² theta - cot² theta = 1. Ok? You must have understood what I mean by that.
123:17 You must have understood what I mean by that. If it says cosec² theta - 1,
123:21 If it says cosec² theta - 1, So instead of that you write directly cot² theta
123:23 So instead of that you write directly cot² theta You can. If it is written somewhere cot² theta
123:26 You can. If it is written somewhere cot² theta So instead you can write cosec² theta - 1
123:28 So instead you can write cosec² theta - 1 yes.
123:30 yes. Ok? What is the use of all this? All
123:33 Ok? What is the use of all this? All I will explain. once before once again
123:35 I will explain. once before once again Let's recall everything. Ok?
123:38 Let's recall everything. Ok? How to remember it roughly? Listen. If
123:42 How to remember it roughly? Listen. If You look here here sin friendship cosec
123:46 You look here here sin friendship cosec Is with me. But here sin is friends with cos
123:50 Is with me. But here sin is friends with cos Is. Listen to what I am saying.
123:53 Is. Listen to what I am saying. Here Sin is friends with Cosec. here
123:55 Here Sin is friends with Cosec. here Sin is friends with cos. So sin
123:58 Sin is friends with cos. So sin You can see two friends. to sin
124:01 You can see two friends. to sin You can convert sin into cosec and sin into cos
124:03 You can convert sin into cosec and sin into cos Can do. Similarly, you can convert cos to sec
124:07 Can do. Similarly, you can convert cos to sec And you can convert cos into sin.
124:10 And you can convert cos into sin. cos also has two friends. If I calculate the number of sec
124:13 cos also has two friends. If I calculate the number of sec If I talk about it, sec also has two friends. sec
124:16 If I talk about it, sec also has two friends. sec You can convert it to cos and sec to
124:18 You can convert it to cos and sec to You can change the tan. So this thing
124:20 You can change the tan. So this thing You should understand. If I believe that
124:23 You should understand. If I believe that One of the trigonometric ratios is tan
124:26 One of the trigonometric ratios is tan So tan theta also had two friends in a way
124:28 So tan theta also had two friends in a way From. You can change tan theta to cot theta.
124:31 From. You can change tan theta to cot theta. Or you can convert tan theta to sec theta
124:35 Or you can convert tan theta to sec theta You can change it. Can't you understand?
124:37 You can change it. Can't you understand? It will come, it will come. Don't worry. I all
124:40 It will come, it will come. Don't worry. I all Let me explain. For now, just remember this much
124:42 Let me explain. For now, just remember this much In which cos can it change?
124:44 In which cos can it change? sin cosec in reciprocal identities
124:47 sin cosec in reciprocal identities in cos sec in tan cot in one and
124:50 in cos sec in tan cot in one and squared runs with sin cos
124:52 squared runs with sin cos commutes with sec tan commutes with cosec cot
124:55 commutes with sec tan commutes with cosec cot and both of these are separately tan sin / cos
124:58 and both of these are separately tan sin / cos cot cos / sin ok now what is the question
125:01 cot cos / sin ok now what is the question Here comes a basic thing that you need to understand.
125:04 Here comes a basic thing that you need to understand. Now you will understand that you
125:06 Now you will understand that you Trigonometric ratios can be used in any other way.
125:09 Trigonometric ratios can be used in any other way. Can change the trigonometric ratio
125:11 Can change the trigonometric ratio Are. You can calculate any trigonometric ratio
125:14 Are. You can calculate any trigonometric ratio into some other trigonometric ratio
125:16 into some other trigonometric ratio You can change it. How is this? We do not understand
125:18 You can change it. How is this? We do not understand Came. I mean, I am explaining. Suppose you
125:22 Came. I mean, I am explaining. Suppose you Give me any trigonometric ratio sin
125:23 Give me any trigonometric ratio sin Theta. Or let's say you gave me sec theta.
125:27 Theta. Or let's say you gave me sec theta. Jan sec theta. You tell me in which
125:30 Jan sec theta. You tell me in which Do you want to change? Any trigonometric
125:32 Do you want to change? Any trigonometric Tell me the ratio and I will change it for you.
125:34 Tell me the ratio and I will change it for you. Let's say you told me. you told me
125:37 Let's say you told me. you told me So change sec theta to cosec theta.
125:39 So change sec theta to cosec theta. What did you say? that sec theta ko brother change
125:42 What did you say? that sec theta ko brother change Show that cosec in theta. Now how do I
125:44 Show that cosec in theta. Now how do I I will change it and see. Basically its
125:46 I will change it and see. Basically its This means that sec theta and cosec theta
125:50 This means that sec theta and cosec theta Create an identity. Make a formula.
125:54 Create an identity. Make a formula. Ok? Now tell me how to do it. To all
125:58 Ok? Now tell me how to do it. To all Who are the friends of the first sec? Tell me this.
126:00 Who are the friends of the first sec? Tell me this. So brother, the reciprocal of sec theta
126:03 So brother, the reciprocal of sec theta Identity has friends cos theta and sec
126:06 Identity has friends cos theta and sec Theta's one-square identity
126:08 Theta's one-square identity I am a friend of tan theta yes and no you see
126:12 I am a friend of tan theta yes and no you see You can here that sec theta is friends with cos
126:15 You can here that sec theta is friends with cos sec theta is friends with theta tan theta
126:17 sec theta is friends with theta tan theta I have written the same thing here.
126:20 I have written the same thing here. Friend, SEC is friends with Cosec.
126:22 Friend, SEC is friends with Cosec. No, SEC is friends with Cosec.
126:24 No, SEC is friends with Cosec. No, it doesn't matter, how will we make friends?
126:27 No, it doesn't matter, how will we make friends? Let's see, I will make some arrangements, okay okay. Now
126:30 Let's see, I will make some arrangements, okay okay. Now Tell me, with whom is Cos friends?
126:33 Tell me, with whom is Cos friends? cos is friends with sec and sin
126:36 cos is friends with sec and sin with. Yes or no? and with sin. tan's
126:41 with. Yes or no? and with sin. tan's Friendship with sec and with cot.
126:45 Friendship with sec and with cot. Yes or no? Yes or no? Now the friendship of sin
126:48 Yes or no? Yes or no? Now the friendship of sin Tell. So the friendship of sin is one and reciprocal
126:50 Tell. So the friendship of sin is one and reciprocal with cosec in one. One and Reciprocal
126:54 with cosec in one. One and Reciprocal with cosec in one. And the Forest and the Square
126:58 with cosec in one. And the Forest and the Square If I talk about cot with cos in Vali
127:01 If I talk about cot with cos in Vali Cot's friendship between one and reciprocal one
127:04 Cot's friendship between one and reciprocal one Sorry with tan in a reciprocal one
127:07 Sorry with tan in a reciprocal one with tan and in one and square one
127:09 with tan and in one and square one with Cossack. So what do you mean by that? to say
127:12 with Cossack. So what do you mean by that? to say I mean, you understand what I am saying.
127:14 I mean, you understand what I am saying. Am. Brother, every person has two friends. every
127:17 Am. Brother, every person has two friends. every A man has two friends. if you think
127:19 A man has two friends. if you think So. Ok? You first noticed that sec
127:23 So. Ok? You first noticed that sec is friends with cos in reciprocal
127:26 is friends with cos in reciprocal So with tan in one and square one
127:28 So with tan in one and square one If it is not with cosec then it does not matter now.
127:30 If it is not with cosec then it does not matter now. If you look at cos, cos is friends with sec
127:32 If you look at cos, cos is friends with sec tan is friends with sin and sec is friends with
127:35 tan is friends with sin and sec is friends with Now let's look at sin with and cot.
127:38 Now let's look at sin with and cot. Sin is friends with cos, so cosec
127:40 Sin is friends with cos, so cosec It is also with . cot's friendship with tan
127:43 It is also with . cot's friendship with tan So it is with cosec also. to say
127:45 So it is with cosec also. to say What does it mean? First convert sec to cos.
127:48 What does it mean? First convert sec to cos. Then sin into cosec. Did you understand? means sec
127:52 Then sin into cosec. Did you understand? means sec First change it to cos, then cos to sin
127:54 First change it to cos, then cos to sin in, then sin in cosec. or to sec
127:57 in, then sin in cosec. or to sec First change tan to cot, then tan to cot
128:00 First change tan to cot, then tan to cot in, then cot in cosec. which makes you easy
128:02 in, then cot in cosec. which makes you easy I feel like doing that. Well, both of them
128:05 I feel like doing that. Well, both of them Friends, it will take the same time. So a job
128:08 Friends, it will take the same time. So a job I will do it a little. First of all, sec
128:11 I will do it a little. First of all, sec First of all I convert sec to cos. Above
128:14 First of all I convert sec to cos. Above I adopt the one. I follow the above.
128:17 I adopt the one. I follow the above. Ok? Now listen carefully and comfortably. Correct
128:19 Ok? Now listen carefully and comfortably. Correct Is? So let's take sec theta so sec
128:23 Is? So let's take sec theta so sec Changing theta to cos is sec theta
128:25 Changing theta to cos is sec theta Your 1 / cos theta is over now cos
128:29 Your 1 / cos theta is over now cos convert cos to sin
128:31 convert cos to sin So write down the identities of cos and sin.
128:34 So write down the identities of cos and sin. cos² theta
128:37 cos² theta + sin² theta 1 then what is the value of cos theta
128:41 + sin² theta 1 then what is the value of cos theta It will come, just see, it has come 1 - sin theta.
128:45 It will come, just see, it has come 1 - sin theta. The value of cos theta is squared
128:48 The value of cos theta is squared go
128:54 1 - sin² is theta plus minus. But I Not taking both the values. Because I
128:56 Not taking both the values. Because I I am studying trigonometry of class 10th.
128:58 I am studying trigonometry of class 10th. Negative values should not be dealt with at all.
129:00 Negative values should not be dealt with at all. Ok? So what do you mean by that? cos theta
129:02 Ok? So what do you mean by that? cos theta You can write instead of
129:04 You can write instead of 1 - sin² theta. Did you understand this? What
129:08 1 - sin² theta. Did you understand this? What Did you understand this? To make all these changes
129:10 Did you understand this? To make all these changes There is a way. So sec is first converted to cos and then to cos
129:12 There is a way. So sec is first converted to cos and then to cos to sin. So I wrote it down.
129:18 to sin. So I wrote it down. 1 - sin² theta Now change sin to cosec
129:23 1 - sin² theta Now change sin to cosec Have to do it. You know that directly
129:24 Have to do it. You know that directly Is. 1 / under root pay attention to 1 - sin²
129:29 Is. 1 / under root pay attention to 1 - sin² Wrote down 1/
129:32 Wrote down 1/ cosec² theta. If you want, LCM to LCM
129:35 cosec² theta. If you want, LCM to LCM Take. 1 / cosec² theta will come here. So
129:39 Take. 1 / cosec² theta will come here. So cosec² theta - 1
129:43 cosec² theta - 1 in the root and down your down your cosec²
129:49 in the root and down your down your cosec² theta
129:51 theta Ok? Simplify a bit. So the forest
129:54 Ok? Simplify a bit. So the forest Plant a forest below. Divided by this is your
129:57 Plant a forest below. Divided by this is your Went
130:05 cosec² theta - 1 / cosec² theta so just go up and this is the bottom
130:08 cosec² theta so just go up and this is the bottom This is yours, it has come to the top.
130:12 This is yours, it has come to the top. cosec² theta by
130:21 cosec² theta - 1 What was to be done? What was to be done? sec theta
130:25 What was to be done? What was to be done? sec theta pay attention. sec theta to cosec theta
130:29 pay attention. sec theta to cosec theta Had to change. You did it. sec theta
130:33 Had to change. You did it. sec theta Had to change to cosec theta. you did
130:36 Had to change to cosec theta. you did Gave. If you want, you can do it here using the square root.
130:40 Gave. If you want, you can do it here using the square root. You can cut this one square.
130:43 You can cut this one square. Ok? Didn't you understand? Something
130:45 Ok? Didn't you understand? Something No. One more and one more. slowly understanding
130:48 No. One more and one more. slowly understanding This thing comes. Come on, if I believe you
130:51 This thing comes. Come on, if I believe you Let me tell you to change sin theta and show tan
130:54 Let me tell you to change sin theta and show tan in theta. Change sin theta and show
130:57 in theta. Change sin theta and show into tan theta. So you have to think about two things.
130:59 into tan theta. So you have to think about two things. First of all, friendship of sin. So sin
131:01 First of all, friendship of sin. So sin friendship with cosec in reciprocal ones
131:04 friendship with cosec in reciprocal ones Is. friendship of sin one and square ones
131:08 Is. friendship of sin one and square ones is with cos . So with tan then
131:12 is with cos . So with tan then Not friendship. No problem. Now cosec's
131:13 Not friendship. No problem. Now cosec's There is friendship with sin. cosec of
131:16 There is friendship with sin. cosec of Friendship is also with cot. friendship of cos
131:20 Friendship is also with cot. friendship of cos is with sin as well as sec. of cot
131:24 is with sin as well as sec. of cot Friendship is with cosec as well as with tan
131:27 Friendship is with cosec as well as with tan Also there. And similarly, the friendship of sec is with cos
131:30 Also there. And similarly, the friendship of sec is with cos It is with me and it is with Tan as well. So
131:33 It is with me and it is with Tan as well. So Similarly, both the beans are going to fall on your
131:37 Similarly, both the beans are going to fall on your You can use it as per your wish. I do one thing
131:39 You can use it as per your wish. I do one thing I'll use this one this time.
131:44 I'll use this one this time. Ok? Do you understand? Ok? So
131:46 Ok? Do you understand? Ok? So So first convert sin into cos, then
131:49 So first convert sin into cos, then cos to sec, then sec to tan. Let us go,
131:52 cos to sec, then sec to tan. Let us go, So how do we convert sin to cos? Attention
131:54 So how do we convert sin to cos? Attention Give. So to convert sin to cos you need
131:58 Give. So to convert sin to cos you need I know the identity. sin² + cos² = 1 so
132:02 I know the identity. sin² + cos² = 1 so sin² theta = 1 - cos² theta. So sin theta
132:08 sin² theta = 1 - cos² theta. So sin theta What is the value of it? + -
132:12 What is the value of it? + - 1 - cos² theta will not take negative values.
132:16 1 - cos² theta will not take negative values. So here is your value of sin theta.
132:20 So here is your value of sin theta. 1 -
132:22 1 - cos² theta. Ok? Now convert sin to cos
132:26 cos² theta. Ok? Now convert sin to cos I changed it. cos has to be converted to sec. So
132:28 I changed it. cos has to be converted to sec. So cos in sec would have been reciprocal
132:30 cos in sec would have been reciprocal Is. So this is easy. So sin theta is your
132:32 Is. So this is easy. So sin theta is your Went
132:33 Went 1 - 1 / sec² theta.
132:37 1 - 1 / sec² theta. Understand?
132:39 Understand? Easy. Ok? Now look up. pay attention.
132:42 Easy. Ok? Now look up. pay attention. Let's simplify this a bit. So sin
132:45 Let's simplify this a bit. So sin theta equal to your if you LCM
132:48 theta equal to your if you LCM If you take sec² theta - 1 / sec² theta.
132:57 If you take sec² theta - 1 / sec² theta. Ok? Easy. Now convert sec to tan sec tan
133:00 Ok? Easy. Now convert sec to tan sec tan I have to do it in sec tan. sec to tan
133:03 I have to do it in sec tan. sec to tan Have to do it. You can also do it directly or
133:06 Have to do it. You can also do it directly or Then how will you write identity? look here
133:09 Then how will you write identity? look here sec has to be converted to tan. Now you
133:10 sec has to be converted to tan. Now you Identity must be known that sec² theta
133:14 Identity must be known that sec² theta is 1 + 1 + tan² theta. This identity
133:20 is 1 + 1 + tan² theta. This identity You know the basic one. Ok? So you
133:22 You know the basic one. Ok? So you Look, instead of sec², write 1 instead of sec²
133:25 Look, instead of sec², write 1 instead of sec² + tan² so instead of sec² you wrote 1 +
133:30 + tan² so instead of sec² you wrote 1 + tan² and -1 you replaced with sec² from before
133:35 tan² and -1 you replaced with sec² from before If you write 1 + tan² then your direct answer is
133:39 If you write 1 + tan² then your direct answer is Comes sin theta =
133:41 Comes sin theta = went from +1 to -1
133:44 went from +1 to -1 tan² theta / 1 + tan² theta to do the same
133:49 tan² theta / 1 + tan² theta to do the same It was said that sin theta is converted to tan tan theta
133:52 It was said that sin theta is converted to tan tan theta Change it. sin theta to tan theta
133:54 Change it. sin theta to tan theta Change it. You can use any trigonometric
133:58 Change it. You can use any trigonometric Ratio can be divided into any other trigonometric ratio.
134:00 Ratio can be divided into any other trigonometric ratio. You can change it in . This is the most important
134:04 You can change it in . This is the most important The thing is. Ok? Do you understand? Sure?
134:08 The thing is. Ok? Do you understand? Sure? Now look at a very simple NCERT book.
134:11 Now look at a very simple NCERT book. Question. Ok? Well, by the way, this is CBSE.
134:13 Question. Ok? Well, by the way, this is CBSE. The question was about 2025. You will remember one that
134:16 The question was about 2025. You will remember one that I told you that in a while
134:18 I told you that in a while I will get it done. Now pay attention. now over here
134:20 I will get it done. Now pay attention. now over here What was it, boss? You already know the value of sin 50°
134:23 What was it, boss? You already know the value of sin 50° Not there. I don't even know sin 50°. Any
134:26 Not there. I don't even know sin 50°. Any No matter. I know sin 30. pay attention
134:29 No matter. I know sin 30. pay attention Now a little. So instead of three sin 30, you write 1/2.
134:33 Now a little. So instead of three sin 30, you write 1/2. Cube of two. Ok? - 4 sin 30 so sin
134:38 Cube of two. Ok? - 4 sin 30 so sin 1/2 its cube instead of 30. Ok?
134:41 1/2 its cube instead of 30. Ok? Divided by. Well, this isn't a cube. These
134:43 Divided by. Well, this isn't a cube. These There is no cube. Divide by look here. Now
134:46 There is no cube. Divide by look here. Now I don't know cos 50 sin 50. No problem.
134:48 I don't know cos 50 sin 50. No problem. If you look at both, two things will be common.
134:51 If you look at both, two things will be common. So what will be left inside? sin² 50
134:55 So what will be left inside? sin² 50 + cos² 50°
134:59 + cos² 50° I do not know the value of
135:02 I do not know the value of Friends, what is sin² theta + cos² theta
135:06 Friends, what is sin² theta + cos² theta Is? What is sin² theta + cos² theta?
135:10 Is? What is sin² theta + cos² theta? The value of this whole thing will become one. As such
135:13 The value of this whole thing will become one. As such Why? Because you guys know you guys
135:16 Why? Because you guys know you guys You know I taught you identity.
135:19 You know I taught you identity. that sin² theta + cos² θ1 means that if sin²
135:23 that sin² theta + cos² θ1 means that if sin² If it is written 20 + cos² 20 then instead of it
135:26 If it is written 20 + cos² 20 then instead of it You can directly write one. If sin² is 50
135:28 You can directly write one. If sin² is 50 If it is written + cos² 50 then you can write it in its place
135:30 If it is written + cos² 50 then you can write it in its place You can write direct one. If sin² + 90
135:34 You can write direct one. If sin² + 90 If it is written cos² 90 then you can directly write it in its place.
135:36 If it is written cos² 90 then you can directly write it in its place. You can write forest. If sin² 1.5° + cos²
135:40 You can write forest. If sin² 1.5° + cos² 1.5° is written. Meaning the angle is the same here.
135:44 1.5° is written. Meaning the angle is the same here. So you can write one in its place also. So
135:46 So you can write one in its place also. So Even if you know sin 50 and cos 50
135:51 Even if you know sin 50 and cos 50 I don't know the value of but if you two common
135:53 I don't know the value of but if you two common If you subtract it, it will become sin² 50 + cos² 51
135:57 If you subtract it, it will become sin² 50 + cos² 51 And then you can solve it. How?
136:00 And then you can solve it. How? Did you feel the question? I enjoyed it. questions of this kind
136:04 Did you feel the question? I enjoyed it. questions of this kind asks CBSE. Okay, right? Come on. now one
136:07 asks CBSE. Okay, right? Come on. now one Let's ask a very basic question from NCERT.
136:09 Let's ask a very basic question from NCERT. Write all the other trigonometric ratios of
136:12 Write all the other trigonometric ratios of Angle A in terms of sec A means what did you say?
136:15 Angle A in terms of sec A means what did you say? Went? All trigonometric ratios
136:18 Went? All trigonometric ratios All trigonometric ratios in seconds
136:21 All trigonometric ratios in seconds Show me how to change it. So first thing to do
136:23 Show me how to change it. So first thing to do We do. Let's change it to sin cosec.
136:26 We do. Let's change it to sin cosec. Ok? First change to sin cosec
136:28 Ok? First change to sin cosec We do. I taught you guys simply
136:32 We do. I taught you guys simply What? Follow the same basic things. sin
136:35 What? Follow the same basic things. sin Friendship with whom? Sin's friendship with forest and
136:38 Friendship with whom? Sin's friendship with forest and square with cos and sin
136:41 square with cos and sin Friendship with cosec in reciprocal one.
136:45 Friendship with cosec in reciprocal one. Then cos is friends with sin.
136:48 Then cos is friends with sin. cos is friends with sec. cosec
136:51 cos is friends with sec. cosec That friendship is with sin. cosec
136:53 That friendship is with sin. cosec He is also friends with cot. Now you
136:56 He is also friends with cot. Now you Look you have to go sin sec sec. from sin
136:59 Look you have to go sin sec sec. from sin You have seen sec, now learn sec from sin.
137:01 You have seen sec, now learn sec from sin. This is the way. Understand? going from sin to sec
137:05 This is the way. Understand? going from sin to sec You found this path. go from sin to sec
137:09 You found this path. go from sin to sec You found this way. meant to say
137:11 You found this way. meant to say What? convert sin to cos cos to sec
137:14 What? convert sin to cos cos to sec In. So brother, you know that sin² a =
137:19 In. So brother, you know that sin² a = Or go to Basic Identity. sin² a +
137:24 Or go to Basic Identity. sin² a + cos² a = 1
137:27 cos² a = 1 So sin² a = 1 - cos² a so sin a
137:33 So sin² a = 1 - cos² a so sin a What is the value?
137:35 What is the value? 1 - cos² a then change sin to cos
137:39 1 - cos² a then change sin to cos Gave. Now convert cos to sec. Then cos
137:42 Gave. Now convert cos to sec. Then cos It will be very easy in seconds.
137:45 It will be very easy in seconds. 1 - cos² a is replaced by cos² a by 1 /
137:50 1 - cos² a is replaced by cos² a by 1 / sec² a If you take LCM from LCM then this is your
137:53 sec² a If you take LCM from LCM then this is your sec² a - 1
137:56 sec² a - 1 / sec² a and this is your under root of sin a
138:00 / sec² a and this is your under root of sin a The value has come in terms of sec a, this is
138:04 The value has come in terms of sec a, this is You changed sin a to sec a. Now
138:06 You changed sin a to sec a. Now sin a is done. Now cos a now cos a then cos a
138:11 sin a is done. Now cos a now cos a then cos a To
138:13 To If you want to change it in sec a then this is very
138:16 If you want to change it in sec a then this is very It's easy. How? You know that cos of
138:20 It's easy. How? You know that cos of friendship one and square one in sin
138:22 friendship one and square one in sin together and in reciprocal one it is sec
138:25 together and in reciprocal one it is sec It happens with. So you understood
138:27 It happens with. So you understood That cos is changing directly into sec.
138:29 That cos is changing directly into sec. How? You wrote cos a as 1 / sec a
138:34 How? You wrote cos a as 1 / sec a That's it.
138:36 That's it. Ok? What is left now? change the sin
138:39 Ok? What is left now? change the sin Given, change cos, change tan
138:41 Given, change cos, change tan Do it. So converting tan a to sec a
138:44 Do it. So converting tan a to sec a Is. Ok? tan a
138:49 Is. Ok? tan a Have to change to sec a. Extremely easy.
138:52 Have to change to sec a. Extremely easy. Boss, with whom is Tan A friends?
138:55 Boss, with whom is Tan A friends? So tan a has friendship. with sec so is
138:58 So tan a has friendship. with sec so is Same one and square one and reciprocal
139:01 Same one and square one and reciprocal The one with cot is in the walli. The second has arrived. So
139:04 The one with cot is in the walli. The second has arrived. So How to convert tan a to sec a directly
139:06 How to convert tan a to sec a directly Can you do it? Using the Identity. then tan
139:09 Can you do it? Using the Identity. then tan And what is the identity of sec? Basic
139:10 And what is the identity of sec? Basic Write down your identity. sec² a = 1 +
139:16 Write down your identity. sec² a = 1 + tan² a You have to convert tan a to sec a
139:19 tan² a You have to convert tan a to sec a Is. Tan a has to be changed to sec a. So
139:21 Is. Tan a has to be changed to sec a. So tan a has to be separated. So do one thing
139:24 tan a has to be separated. So do one thing that sec² a - 1 = tan² a now we need tan a
139:30 that sec² a - 1 = tan² a now we need tan a The value of tan a is obtained.
139:34 The value of tan a is obtained. The value of tan a is obtained. The square went there
139:37 The value of tan a is obtained. The square went there So
139:44 sec² a - 1 so look at tan a in sec a How easily you changed it. What is left now?
139:47 How easily you changed it. What is left now? Now your left cosec a
139:51 Now your left cosec a cosec a has to be changed to sec a. Very
139:56 cosec a has to be changed to sec a. Very Much easier. With whom is Cossack's friendship?
139:58 Much easier. With whom is Cossack's friendship? with? So cosec's friendship with reciprocal ones
140:02 with? So cosec's friendship with reciprocal ones in with sin a and square one and
140:05 in with sin a and square one and with cot in the squared one then sin
140:09 with cot in the squared one then sin Friendship with cosec brother, look at sec
140:11 Friendship with cosec brother, look at sec If sec is not found then sin is not found
140:12 If sec is not found then sin is not found friendship of cosec with cos and cot with cos
140:16 friendship of cosec with cos and cot with cos friendship with cosec and the same with tan
140:20 friendship with cosec and the same with tan The thing is cos is friends with sin and with sec
140:24 The thing is cos is friends with sin and with sec Tan's friendship with cot and with sec
140:27 Tan's friendship with cot and with sec with
140:29 with Ok? So now you guys can also direct this.
140:31 Ok? So now you guys can also direct this. You can. any problem any trouble
140:34 You can. any problem any trouble Not there. Ok? How? What you just taught
140:36 Not there. Ok? How? What you just taught I asked you guys what will you do? First of all
140:38 I asked you guys what will you do? First of all Suppose you have this form of cosec or
140:41 Suppose you have this form of cosec or What will have to be done if this thing is adopted?
140:43 What will have to be done if this thing is adopted? First convert cosec to cot, cot to tan
140:45 First convert cosec to cot, cot to tan in, tan in sec. or a direct
140:48 in, tan in sec. or a direct Tell me the method. This is the direct method. Me
140:52 Tell me the method. This is the direct method. Me Tell me cosec is the reciprocal of what?
140:54 Tell me cosec is the reciprocal of what? cosec is the reciprocal of sin. of sin
140:58 cosec is the reciprocal of sin. of sin It is reciprocal. Meaning whatever sin comes
141:00 It is reciprocal. Meaning whatever sin comes Reciprocate it. That would be cos. Who
141:03 Reciprocate it. That would be cos. Who You will also get sin, reciprocate it. They
141:05 You will also get sin, reciprocate it. They cos will come. to say means to say if
141:08 cos will come. to say means to say if Let me ask you directly that cosec a
141:11 Let me ask you directly that cosec a Change it to sec a. so cosec a of you
141:14 Change it to sec a. so cosec a of you Do you know the direct value, can you write it?
141:16 Do you know the direct value, can you write it? sec² a
141:24 sec² a turn it up and sec² a - 1 down. That's it. These are yours
141:29 sec² a - 1 down. That's it. These are yours The value of cosec a is given. to do this thing
141:32 The value of cosec a is given. to do this thing There is no need. Why? Because brother who
141:36 There is no need. Why? Because brother who Brother, suppose if sin a was 1/2 then cosec a would be 2
141:39 Brother, suppose if sin a was 1/2 then cosec a would be 2 / 1 would have happened. If sin a was 1/5 then cosec
141:42 / 1 would have happened. If sin a was 1/5 then cosec a would have been 5 / 1. Whatever its reciprocal sin
141:44 a would have been 5 / 1. Whatever its reciprocal sin Its reciprocal is sin. Its
141:47 Its reciprocal is sin. Its Reciprocal means this above and this below. So
141:50 Reciprocal means this above and this below. So Here comes cosec a. What is left now? Now
141:53 Here comes cosec a. What is left now? Now What's left brother? Sin is done in sec. cos
141:56 What's left brother? Sin is done in sec. cos Done in seconds. It is done in tan tan sec.
142:01 Done in seconds. It is done in tan tan sec. It was done in cosec sec. cot to sec
142:03 It was done in cosec sec. cot to sec It remains to be done. cot a in sec remaining
142:07 It remains to be done. cot a in sec remaining Is. Now you guys tell me in the comment box.
142:11 Is. Now you guys tell me in the comment box. Before proceeding further, tell us in the comment section.
142:14 Before proceeding further, tell us in the comment section. Before moving ahead, its answer is direct
142:16 Before moving ahead, its answer is direct How will you remove it? The value of cot a is sec a
142:19 How will you remove it? The value of cot a is sec a How will you take it out directly in terms?
142:21 How will you take it out directly in terms? This is one way, but is it any easier?
142:24 This is one way, but is it any easier? And is there any faster way than this? Comment
142:28 And is there any faster way than this? Comment Tell in the box. Ok? hashtag
142:31 Tell in the box. Ok? hashtag Please comment brother. Ok? whose
142:34 Please comment brother. Ok? whose If you like the comment, I will try to like it.
142:36 If you like the comment, I will try to like it. I will do it. Ok? So let's move ahead now.
142:39 I will do it. Ok? So let's move ahead now. Now let's talk about the main issue. Let's go now
142:42 Now let's talk about the main issue. Let's go now Let's quickly look at some basic questions. Correct
142:44 Let's quickly look at some basic questions. Correct Is? Now look at you, every question is the same.
142:47 Is? Now look at you, every question is the same. Will come. Prove the following identity that prove
142:50 Will come. Prove the following identity that prove Show me how. There are three ways to proofread.
142:52 Show me how. There are three ways to proofread. But of these three, we will only discuss the first one.
142:54 But of these three, we will only discuss the first one. Will follow. Understand this. Brother, you have two
142:57 Will follow. Understand this. Brother, you have two will be the sides of the equation. Either you take the LHS
143:01 will be the sides of the equation. Either you take the LHS Solve it. Bring RHS. So you
143:05 Solve it. Bring RHS. So you You can say that Hans proved it. Favorite Word
143:08 You can say that Hans proved it. Favorite Word It happens brother. Hans Proved. either you
143:11 It happens brother. Hans Proved. either you Pick up the RHS and you solve it.
143:14 Pick up the RHS and you solve it. Keep doing it, keep doing it and bring LHS
143:17 Keep doing it, keep doing it and bring LHS Go. Then you can say that Hans
143:21 Go. Then you can say that Hans Proved 0.01% in either question
143:24 Proved 0.01% in either question You will have to do this in questions and
143:27 You will have to do this in questions and Where will it have to be done? How will we know? I
143:30 Where will it have to be done? How will we know? I will tell you to solve the LHS as well and
143:34 will tell you to solve the LHS as well and Solve the RHS also. solve this
143:37 Solve the RHS also. solve this Will you do it? As if two has come. will you solve this
143:40 Will you do it? As if two has come. will you solve this As if two has come. So LHS equals RHS so
143:44 As if two has come. So LHS equals RHS so You can also say Hans Proved. to do on
143:46 You can also say Hans Proved. to do on What is? 99.99%
143:50 What is? 99.99% You have to do this thing in the question.
143:52 You have to do this thing in the question. Some 0 Something Something in Percent Questions
143:55 Some 0 Something Something in Percent Questions You will have to do this thing. this thing
143:57 You will have to do this thing. this thing You can do it if you want. But I will advise
143:59 You can do it if you want. But I will advise Do not do it. Ok? Start anyway. Now
144:02 Do not do it. Ok? Start anyway. Now What to do? See how to use your brain?
144:04 What to do? See how to use your brain? How to think? This is important. Ok?
144:07 How to think? This is important. Ok? I am saying one thing, just be patient. 101
144:10 I am saying one thing, just be patient. 101 Be patient with the questions. After that
144:13 Be patient with the questions. After that You might find yourself having to create questions.
144:15 You might find yourself having to create questions. Will take. 10-15 questions at least. Correct
144:18 Will take. 10-15 questions at least. Correct Is? I will get a lot done. all of them
144:20 Is? I will get a lot done. all of them I will get you previous year questions done. Tension
144:22 I will get you previous year questions done. Tension Don't take it. Ok? Let us go. So man LHS
144:25 Don't take it. Ok? Let us go. So man LHS What is given in it? You have a left hand
144:27 What is given in it? You have a left hand Something like this is given on the side. You need this
144:29 Something like this is given on the side. You need this You have to solve it and get one. By solving this
144:31 You have to solve it and get one. By solving this Have to bring the forest. Ok? So how to start
144:33 Have to bring the forest. Ok? So how to start Is? I have to talk to the right hand side.
144:35 Is? I have to talk to the right hand side. Have to bring a good forest. Have to bring a good forest. Correct
144:38 Have to bring a good forest. Have to bring a good forest. Correct Is. Now we have to bring the forest, what would that mean?
144:40 Is. Now we have to bring the forest, what would that mean? Trigonometric ratios are canceling out
144:42 Trigonometric ratios are canceling out Will be. Brother obviously sin² sec² is decreasing
144:45 Will be. Brother obviously sin² sec² is decreasing Only then will the forest come. all of them
144:48 Only then will the forest come. all of them Trigonometric ratios are canceling out
144:49 Trigonometric ratios are canceling out Will be. Now when does anything get cancelled?
144:52 Will be. Now when does anything get cancelled? Remember when she is a bean. meant to say
144:55 Remember when she is a bean. meant to say Brother, if you change sin² to sec²
144:58 Brother, if you change sin² to sec² Or maybe change sec² to sin²
145:01 Or maybe change sec² to sin² These may be cancelled. Brother, from two to two
145:04 These may be cancelled. Brother, from two to two It will be cancelled. will cancel with π only. sin
145:06 It will be cancelled. will cancel with π only. sin Theta sin theta will cancel itself out. So
145:08 Theta sin theta will cancel itself out. So Things get cancelled when they are the same.
145:11 Things get cancelled when they are the same. Ok? Now what's going on here?
145:13 Ok? Now what's going on here? Now what's going on here? here
145:15 Now what's going on here? here One must keep in mind that Boss Sin² should either
145:18 One must keep in mind that Boss Sin² should either Do it in sec². So sec² can be written as either sin²
145:21 Do it in sec². So sec² can be written as either sin² I do it. Now I have taught you that
145:24 I do it. Now I have taught you that How to convert sin into sec. sin of two
145:28 How to convert sin into sec. sin of two I am a friend. Sin has a friend named cos. One
145:32 I am a friend. Sin has a friend named cos. One Friend is a friend cosec. a friend of cos
145:36 Friend is a friend cosec. a friend of cos sin and a friend is sec. cosec one
145:38 sin and a friend is sec. cosec one There is a friend sin and a friend cot. Now listen
145:41 There is a friend sin and a friend cot. Now listen Stop. I will also give you the easy way.
145:43 Stop. I will also give you the easy way. But first listen to me. So the same thing as sin
145:46 But first listen to me. So the same thing as sin cos to cos to sec sin to cos
145:49 cos to cos to sec sin to cos cos sec sin cos cos
145:52 cos sec sin cos cos in sec then sin will change to sec then
145:54 in sec then sin will change to sec then I will speak to you again I will speak to you again
145:55 I will speak to you again I will speak to you again listen to me sin to cos to cos to sec
146:00 listen to me sin to cos to cos to sec I mean your sin has changed to sec
146:03 I mean your sin has changed to sec If your sin changes to sec then maybe
146:06 If your sin changes to sec then maybe I don't understand, it should be cancelled, wait.
146:08 I don't understand, it should be cancelled, wait. You should roughly understand that sin
146:11 You should roughly understand that sin Now change sin to cos
146:13 Now change sin to cos You must remember your identity to make changes to
146:15 You must remember your identity to make changes to It comes. Which one? converting sin to cos
146:18 It comes. Which one? converting sin to cos The identity for is cos² theta + sin²
146:22 The identity for is cos² theta + sin² theta = 1 so you will see here that
146:26 theta = 1 so you will see here that 1 - sin² is how you will write it in the exam.
146:30 1 - sin² is how you will write it in the exam. hand side left hand side. So first of all
146:33 hand side left hand side. So first of all You wrote 1 - sin² theta and here you have
146:37 You wrote 1 - sin² theta and here you have written sec² theta. Now what is 1 - sin² theta
146:40 written sec² theta. Now what is 1 - sin² theta It happens? Look brother, if sin² goes there then 1 -
146:44 It happens? Look brother, if sin² goes there then 1 - What will become sin²? cos²
146:47 What will become sin²? cos² theta and your sec² theta over here. Now sin
146:51 theta and your sec² theta over here. Now sin converted to cos . How to convert cos to sec
146:54 converted to cos . How to convert cos to sec do? You can write cos² as 1 / sec²
146:58 do? You can write cos² as 1 / sec² theta and sec² theta over here. So what did I
147:00 theta and sec² theta over here. So what did I Did you say? When do things get cancelled? When beans
147:02 Did you say? When do things get cancelled? When beans it occurs. So sec² went to sec². Answer One.
147:05 it occurs. So sec² went to sec². Answer One. Write here is equal to RHS. Hens
147:09 Write here is equal to RHS. Hens Proved.
147:11 Proved. Did you understand? If the mind works directly
147:13 Did you understand? If the mind works directly And what's nice is that Boss 1 - sin²
147:16 And what's nice is that Boss 1 - sin² It happens. cos² cos² is 1 / sec² sec²
147:19 It happens. cos² cos² is 1 / sec² sec² sec² removed. I will tell you very easily
147:22 sec² removed. I will tell you very easily In starting. Don't worry boss.
147:24 In starting. Don't worry boss. What should I bring again? Forest. What to bring? Forest.
147:26 What should I bring again? Forest. What to bring? Forest. So things are getting cancelled to bring the forest
147:28 So things are getting cancelled to bring the forest Must be. When do things get cancelled? When beans
147:31 Must be. When do things get cancelled? When beans Are there. Meaning either cos² into tan²,
147:34 Are there. Meaning either cos² into tan², tan² into cos². So think about that now
147:38 tan² into cos². So think about that now Hear Listen here. Ok? Who's who of tan
147:40 Hear Listen here. Ok? Who's who of tan Are you friends? sec and cot sec and cot sec
147:47 Are you friends? sec and cot sec and cot sec You can change it to cos. speak again
147:49 You can change it to cos. speak again I am listening brother. Tan's friendship with sec
147:54 I am listening brother. Tan's friendship with sec friendship of with and cot with and sec cos
147:59 friendship of with and cot with and sec cos With. That means convert tan into sec.
148:03 With. That means convert tan into sec. Convert sec to cos. Do tan in sec.
148:05 Convert sec to cos. Do tan in sec. Convert sec to cos. cos may be cos
148:08 Convert sec to cos. cos may be cos It should be cancelled. So converting tan to sec
148:10 It should be cancelled. So converting tan to sec Is. tan has to be converted to sec. Identity
148:12 Is. tan has to be converted to sec. Identity Which one did you remember? sec and tan ones. then write
148:14 Which one did you remember? sec and tan ones. then write Let's say sec² theta is 1 + tan² theta.
148:21 Let's say sec² theta is 1 + tan² theta. You should know this identity. Just now
148:24 You should know this identity. Just now Write. So brother, you wrote on the left hand side.
148:27 Write. So brother, you wrote on the left hand side. First of all, take this step here.
148:30 First of all, take this step here. Take. What about the second step after that? You
148:33 Take. What about the second step after that? You Look at cos² instead of theta as it is 1 + tan²
148:37 Look at cos² instead of theta as it is 1 + tan² Can you write instead of 1 + tan²?
148:42 Can you write instead of 1 + tan²? sec² theta and you should understand that
148:46 sec² theta and you should understand that You can write this cos² theta sec² as 1 /
148:50 You can write this cos² theta sec² as 1 / cos² or you could also do cos²
148:53 cos² or you could also do cos² Write down 1 / sec² cos².
148:56 Write down 1 / sec² cos². sec² sec² sec² will be deducted. cos² to cos²
148:59 sec² sec² sec² will be deducted. cos² to cos² Gaya = 1 equal to right hand side. Hens
149:04 Gaya = 1 equal to right hand side. Hens Proven
149:06 Proven You can understand it directly also. 1 + tan² sec²
149:09 You can understand it directly also. 1 + tan² sec² sec² * cos² is one. What do you say next?
149:13 sec² * cos² is one. What do you say next? Are you? What are you saying, why is this happening?
149:16 Are you? What are you saying, why is this happening? Are you doing it, friend? Why is this blur coming?
149:19 Are you doing it, friend? Why is this blur coming? Why is this blurry? why is this
149:23 Why is this blurry? why is this Blur is the? no that's ok. Let's talk about anything
149:25 Blur is the? no that's ok. Let's talk about anything No. Anyway, let's go. So what are you saying friend
149:27 No. Anyway, let's go. So what are you saying friend Pay attention to what you are saying here.
149:30 Pay attention to what you are saying here. You guys might be seeing it clearly
149:31 You guys might be seeing it clearly Yes, it is clear to you guys, okay anyway.
149:32 Yes, it is clear to you guys, okay anyway. Look here now friend, I have to bring the forest back to the forest.
149:36 Look here now friend, I have to bring the forest back to the forest. To bring it means everything here is cancelled.
149:38 To bring it means everything here is cancelled. When will things get cancelled when
149:40 When will things get cancelled when If the sum is same then either cot is converted to cos
149:42 If the sum is same then either cot is converted to cos Make two cos into cot as per your wish
149:44 Make two cos into cot as per your wish Now I direct, I direct
149:45 Now I direct, I direct I do it like you wrote first
149:48 I do it like you wrote first In LHS you did this step
149:51 In LHS you did this step I took this step in a second.
149:53 I took this step in a second. Step kya hogi cos² theta θ as it is
149:57 Step kya hogi cos² theta θ as it is Plus, at rest, 1 / 1 + cot² comes to mind
150:01 Plus, at rest, 1 / 1 + cot² comes to mind should be 1 + cot² equals cosec² theta and
150:06 should be 1 + cot² equals cosec² theta and What was the benefit? What was the benefit? 1 /
150:10 What was the benefit? What was the benefit? 1 / cosec² is 1 / cosec² sin² theta and
150:15 cosec² is 1 / cosec² sin² theta and cos² theta + sin² theta is one. Hens
150:19 cos² theta + sin² theta is one. Hens Proved.
150:24 Ok? What did I say? 15 questions. Only three questions have been asked so far. without 15
150:27 Only three questions have been asked so far. without 15 No one will leave the question unanswered. 15
150:29 No one will leave the question unanswered. 15 Have to wait till the question. Have to be patient.
150:31 Have to wait till the question. Have to be patient. I guarantee it will be made. By doing this
150:33 I guarantee it will be made. By doing this It happens. This happens by doing it. This one time
150:35 It happens. This happens by doing it. This one time It is not made in. You will stay. you
150:38 It is not made in. You will stay. you Will maintain patience. You will be patient. you will become
150:40 Will maintain patience. You will be patient. you will become See. Ok? Again, now the mind is here too
150:42 See. Ok? Again, now the mind is here too We should go. Ok? That friend -1 has to be brought.
150:45 We should go. Ok? That friend -1 has to be brought. Meaning things will be getting cancelled here.
150:47 Meaning things will be getting cancelled here. To cancel things. sin² can be divided by either
150:49 To cancel things. sin² can be divided by either convert cot to square, cot² to sin²
150:51 convert cot to square, cot² to sin² Do it. What did I think? sin of two
150:54 Do it. What did I think? sin of two I am a friend. Sin has two friends. cosec and
150:56 I am a friend. Sin has two friends. cosec and of cos cosec and cos cosec and cos cosec
150:58 of cos cosec and cos cosec and cos cosec The friend is cot. You may or may not understand.
151:01 The friend is cot. You may or may not understand. See, first convert sin into cosec
151:05 See, first convert sin into cosec Two. Then change cosec to cot. So
151:08 Two. Then change cosec to cot. So Sin your cot has changed. sin your
151:11 Sin your cot has changed. sin your There was a change in the cot. Meaning sin to cosec
151:14 There was a change in the cot. Meaning sin to cosec In. sin to cosec then cosec to cot
151:16 In. sin to cosec then cosec to cot In. Now how do I convert sin to cosec? You
151:18 In. Now how do I convert sin to cosec? You You can also do it directly. Look at the LHS of the
151:21 You can also do it directly. Look at the LHS of the First this step is second, isn't it?
151:23 First this step is second, isn't it? Step here you wrote cot² theta what
151:27 Step here you wrote cot² theta what Written cot² theta - 1 / sin² is 1 /
151:32 Written cot² theta - 1 / sin² is 1 / sin² is cosec² theta now you here
151:36 sin² is cosec² theta now you here Notice this you have cot² theta minus now
151:40 Notice this you have cot² theta minus now What is cosec² theta? 1 + cot² theta
151:45 What is cosec² theta? 1 + cot² theta What is cosec² theta? 1 + cot² theta
151:48 What is cosec² theta? 1 + cot² theta You should remember this identity.
151:50 You should remember this identity. It should be right in the fingers. Three
151:52 It should be right in the fingers. Three Identities at least that cosec² theta
151:55 Identities at least that cosec² theta is 1 + cot² theta open the brackets. So
151:58 is 1 + cot² theta open the brackets. So cot² theta. Well, by the way, single here.
152:00 cot² theta. Well, by the way, single here. It was the term. There are two terms here, so brackets
152:02 It was the term. There are two terms here, so brackets Have put. -1
152:05 Have put. -1 - cot² of theta plus cot² to the minus cot²
152:09 - cot² of theta plus cot² to the minus cot² Went. -1 left which is on the right hand side
152:12 Went. -1 left which is on the right hand side Is equal. Hens
152:16 Is equal. Hens Ok? Just watch, just watch, just watch
152:18 Ok? Just watch, just watch, just watch Go. Ok? What is he saying next? As such
152:20 Go. Ok? What is he saying next? As such Some say that the boss has given this. You have to bring
152:24 Some say that the boss has given this. You have to bring Forest. You have to bring the forest. Ok? So brother sin
152:28 Forest. You have to bring the forest. Ok? So brother sin Change theta to either tan, tan
152:31 Change theta to either tan, tan Convert theta to either sin. yours
152:33 Convert theta to either sin. yours Will. Ok? Ok? Now look here
152:37 Will. Ok? Ok? Now look here What am I doing? Left Hand Side
152:40 What am I doing? Left Hand Side pay attention. Left hand side 1 + 1 + tan²
152:47 pay attention. Left hand side 1 + 1 + tan² Let Theta be written as it is. 1 + tan²
152:51 Let Theta be written as it is. 1 + tan² Theta as it is. Ok? a + b * a - b
152:55 Theta as it is. Ok? a + b * a - b Many. a + b * a brother this 1 1 this plus
152:59 Many. a + b * a brother this 1 1 this plus what would have been minus this sign sign a + b a - b
153:02 what would have been minus this sign sign a + b a - b Is? a²
153:04 Is? a² - b² a² - b² See what benefit came from this
153:09 - b² a² - b² See what benefit came from this Here 1 + tan² theta is sec² theta - 1
153:15 Here 1 + tan² theta is sec² theta - 1 sin² theta is cos² theta sec² theta
153:20 sin² theta is cos² theta sec² theta You wrote 1 / cos² theta here cos²
153:24 You wrote 1 / cos² theta here cos² Theta has already gone from cos² to cos², this is your
153:26 Theta has already gone from cos² to cos², this is your The forest that you had to bring has arrived.
153:31 The forest that you had to bring has arrived. Ok? It's just a game. like a game
153:34 Ok? It's just a game. like a game If you do the questions, you will become more interested.
153:36 If you do the questions, you will become more interested. Stay tuned. Don't have to go now. Have to do it. Now!
153:39 Stay tuned. Don't have to go now. Have to do it. Now! So very basic, from the very basic level.
153:42 So very basic, from the very basic level. I am getting things done. Ok? Come on now friend
153:44 I am getting things done. Ok? Come on now friend What brain will work here? Here you
153:46 What brain will work here? Here you Have to bring sec. Now listen to me carefully.
153:49 Have to bring sec. Now listen to me carefully. Focus first. Well, sec theta is to be brought.
153:52 Focus first. Well, sec theta is to be brought. sec theta. I will give you an advice
153:54 sec theta. I will give you an advice I do. One what that sin cos things in
153:57 I do. One what that sin cos things in Think about it. thought things out in sin cos
153:59 Think about it. thought things out in sin cos do it. Ok? because all
154:00 do it. Ok? because all Trigonometric ratios in sin cos
154:02 Trigonometric ratios in sin cos Changes happen. Think of it in terms of sin cos
154:05 Changes happen. Think of it in terms of sin cos do it. So brother, you want to bring sec², what does it mean to bring?
154:08 do it. So brother, you want to bring sec², what does it mean to bring? Is? 1 / cos² will have to be brought. Isn't it brother? 1 /
154:12 Is? 1 / cos² will have to be brought. Isn't it brother? 1 / cos² means sec² 1 / cos² means sec² then if
154:15 cos² means sec² 1 / cos² means sec² then if To find sec² means to find 1 / cos².
154:18 To find sec² means to find 1 / cos². If you want to find sec², then you need to find 1/cos².
154:21 If you want to find sec², then you need to find 1/cos². Will have to.
154:22 Will have to. Isn't it? means changing things into cos
154:25 Isn't it? means changing things into cos Is. Meaning the left hand side here is cos
154:28 Is. Meaning the left hand side here is cos I have to make a change. Have to change it to cos.
154:30 I have to make a change. Have to change it to cos. Have to change it to cos. Do you understand this?
154:32 Have to change it to cos. Do you understand this? I? I will say it once again. sec² means 1 /
154:34 I? I will say it once again. sec² means 1 / cos² means left hand side in cos²
154:38 cos² means left hand side in cos² I have to change it. Ok, good. Left Hand
154:40 I have to change it. Ok, good. Left Hand Side sin is given. What is sin to cos
154:42 Side sin is given. What is sin to cos Can I make changes in it? absolutely get it done
154:44 Can I make changes in it? absolutely get it done Can. There may be a change in sin cos.
154:47 Can. There may be a change in sin cos. Sin cosec may change. Then sin
154:50 Sin cosec may change. Then sin square to change to cos
154:52 square to change to cos It is necessary. a little bit a little bit a little bit
154:55 It is necessary. a little bit a little bit a little bit Very lightly. Ok? Anyway Point Ye
154:57 Very lightly. Ok? Anyway Point Ye I understood that I have to change it to cos.
155:00 I understood that I have to change it to cos. Ok? Friend, what should I do? Now tell me if
155:02 Ok? Friend, what should I do? Now tell me if What would have been written as 1/2 + 1/3? If I
155:05 What would have been written as 1/2 + 1/3? If I I would like to tell you what would happen if I asked you to do this. To all
155:08 I would like to tell you what would happen if I asked you to do this. To all What comes to mind first? Taking the LCM. So
155:10 What comes to mind first? Taking the LCM. So Here also you should keep in mind taking LCM.
155:13 Here also you should keep in mind taking LCM. Needed It doesn't matter if it doesn't work out how
155:16 Needed It doesn't matter if it doesn't work out how I am teaching you to take it. Don't worry. 1
155:18 I am teaching you to take it. Don't worry. 1 + sin 1 - sin will be the LCM. 1 + sin *
155:23 + sin 1 - sin will be the LCM. 1 + sin * 1 - sin 1 + sin * 1 - sin What came up
155:27 1 - sin 1 + sin * 1 - sin What came up Will you go? Have to focus. Ok? 1+ here
155:30 Will you go? Have to focus. Ok? 1+ here sin here 1 + sin here 1 + sin here
155:33 sin here 1 + sin here 1 + sin here What is left over 1 + sin? This is it above
155:35 What is left over 1 + sin? This is it above Multiply it. So going into the forest 1 - sin
155:39 Multiply it. So going into the forest 1 - sin theta multiplied in the middle plus 1 over here -
155:42 theta multiplied in the middle plus 1 over here - sin here 1 - sin here 1 - sin here
155:44 sin here 1 - sin here 1 - sin here 1 - sin what is left, this is above
155:46 1 - sin what is left, this is above multiply it by 1 * 1 + sin theta whatever
155:51 multiply it by 1 * 1 + sin theta whatever You have to bring it. Ok? Now just solve it.
155:54 You have to bring it. Ok? Now just solve it. So going into one, this becomes your 1 - sinθ.
155:57 So going into one, this becomes your 1 - sinθ. Will go. This becomes your 1 + sin theta.
156:00 Will go. This becomes your 1 + sin theta. what's down? If you pay attention, a + b
156:03 what's down? If you pay attention, a + b * a - b is a² - b² ok minus
156:10 * a - b is a² - b² ok minus sine plus sine of 1 + 1 2 1 - sin²
156:14 sine plus sine of 1 + 1 2 1 - sin² cos²
156:16 cos² theta is 1 - sin² cos² theta answer
156:20 theta is 1 - sin² cos² theta answer Bhai from Gaya should I put 2 * 1 with two and 1
156:24 Bhai from Gaya should I put 2 * 1 with two and 1 / cos² is what is sec² so 2 sec² is theta
156:30 / cos² is what is sec² so 2 sec² is theta The answer has come which is on the right hand side
156:32 The answer has come which is on the right hand side Is equal. So Hans
156:35 Is equal. So Hans Proven
156:38 Proven What comes to mind first?
156:41 What comes to mind first? Brother? Look, sec means sec means 1 / cos sec
156:44 Brother? Look, sec means sec means 1 / cos sec Meaning 1 / cos means cos is to be brought. means these
156:48 Meaning 1 / cos means cos is to be brought. means these All things have to be changed to cos. Some?
156:50 All things have to be changed to cos. Some? So it is already in cos. sin to cos
156:53 So it is already in cos. sin to cos I have to change it. What will come to mind most
156:54 I have to change it. What will come to mind most First? To simplify. Simplification
156:57 First? To simplify. Simplification Taking LCM, Adding, Multiplying in
156:59 Taking LCM, Adding, Multiplying in to do. Opening the brackets covers all this. So
157:02 to do. Opening the brackets covers all this. So The first thing that comes to your mind is probably LCM.
157:05 The first thing that comes to your mind is probably LCM. I will come to take it. So the LCM of 1 - sin 1 + sin
157:09 I will come to take it. So the LCM of 1 - sin 1 + sin The same will come out to 1 - sin * 1 + sin. looking up
157:15 The same will come out to 1 - sin * 1 + sin. looking up What will come? Easy on top. Ok? So 1 -
157:17 What will come? Easy on top. Ok? So 1 - sin 1 - sin 1 is left. Multiply this up
157:21 sin 1 - sin 1 is left. Multiply this up So costtheta * 1 + sinθ bracket proper
157:25 So costtheta * 1 + sinθ bracket proper Put a plus. 1 + sin 1 + sin 1 + sin 1 +
157:28 Put a plus. 1 + sin 1 + sin 1 + sin 1 + What is left? This is 1 - sin so cos theta
157:31 What is left? This is 1 - sin so cos theta What multiply 1 - sinθ over here, whatever
157:35 What multiply 1 - sinθ over here, whatever If you want to bring it, it will come automatically. Ok?
157:38 If you want to bring it, it will come automatically. Ok? So cos theta goes in so cos theta * 1 cos
157:41 So cos theta goes in so cos theta * 1 cos theta cos theta * sinθ cosθ sin theta + cos
157:46 theta cos theta * sinθ cosθ sin theta + cos theta * 1 cos theta cos theta * sin theta is
157:51 theta * 1 cos theta cos theta * sin theta is cos theta sin theta down what down same
157:55 cos theta sin theta down what down same what a - b a + b is a² - b² now you understand
158:02 what a - b a + b is a² - b² now you understand loge plus cosin minus cos sin cot
158:05 loge plus cosin minus cos sin cot Brother, this is also cos sin, this is also cos sin
158:08 Brother, this is also cos sin, this is also cos sin This is plus, it is divided by minus. So cos
158:10 This is plus, it is divided by minus. So cos + cos 2 cos theta 1 - sin²
158:15 + cos 2 cos theta 1 - sin² theta is cos² theta. Now you are a little
158:19 theta is cos² theta. Now you are a little Imagine if you can, what cos² theta means.
158:21 Imagine if you can, what cos² theta means. cos theta * cos theta. So 1 cos theta to one
158:24 cos theta * cos theta. So 1 cos theta to one cos theta went. So this is your 2 / cos theta *
158:29 cos theta went. So this is your 2 / cos theta * Write 1. No problem. So 1 / cos
158:32 Write 1. No problem. So 1 / cos What is theta? sec theta. Your
158:33 What is theta? sec theta. Your The answer is 2sc theta which is what you wanted.
158:38 The answer is 2sc theta which is what you wanted. Hans Proved.
158:40 Hans Proved. Ok? Keep doing it easy. Just keep doing it. stop it
158:43 Ok? Keep doing it easy. Just keep doing it. stop it Two. Okay, now these are a little special type.
158:46 Two. Okay, now these are a little special type. There are questions about this. Now here too
158:47 There are questions about this. Now here too Think in such a sin cos way brother, this is what happens
158:49 Think in such a sin cos way brother, this is what happens is 1 / cos or sin / cos yes or
158:52 is 1 / cos or sin / cos yes or No? This is 1 / cos, this is sin /
158:55 No? This is 1 / cos, this is sin / cos means roughly above, sin below
158:58 cos means roughly above, sin below cos is needed. Need sin above, cos below
159:00 cos is needed. Need sin above, cos below Need, sin above, cos below and
159:03 Need, sin above, cos below and The root has to be removed. Need sin above, cos below
159:06 The root has to be removed. Need sin above, cos below and remove the root. Meaning in sin cos
159:08 and remove the root. Meaning in sin cos We have to keep things as they are. Ok? How to Root
159:11 We have to keep things as they are. Ok? How to Root Should I remove it? Now a special thing to remove the root
159:13 Should I remove it? Now a special thing to remove the root We do. Listen carefully. remember you remember
159:15 We do. Listen carefully. remember you remember There will be rationalization in the ninth class. By the way
159:17 There will be rationalization in the ninth class. By the way I will do something here. Left Hand Side
159:20 I will do something here. Left Hand Side How are you solving it? pay attention. Correct
159:22 How are you solving it? pay attention. Correct Is? I wrote Under Root.
159:24 Is? I wrote Under Root. This is written here as 1 - sin theta. written below
159:28 This is written here as 1 - sin theta. written below is 1 + sin theta. What did I do to myself?
159:31 is 1 + sin theta. What did I do to myself? Hear What did I do to myself up and down
159:33 Hear What did I do to myself up and down Multiply it?
159:35 Multiply it? 1 - sin theta and 1 - sin theta. Understand?
159:40 1 - sin theta and 1 - sin theta. Understand? Why so? If 1 plus is written here then
159:42 Why so? If 1 plus is written here then Up by 1 - sin Down by 1 - sin
159:44 Up by 1 - sin Down by 1 - sin Multiply. I can do this. Above
159:46 Multiply. I can do this. Above Multiply with the same thing below. Now from this
159:48 Multiply with the same thing below. Now from this What was the benefit? 1 - sin theta * 1 - sin
159:51 What was the benefit? 1 - sin theta * 1 - sin Theta. Can I divide this by 1 - sinθ squared?
159:55 Theta. Can I divide this by 1 - sinθ squared? I can't write brother. a * a² 2 * 2 2² b * b
160:01 I can't write brother. a * a² 2 * 2 2² b * b b² c * c² 4 * 4 4² so 1 - 9 * 1 - 9 1 -
160:07 b² c * c² 4 * 4 4² so 1 - 9 * 1 - 9 1 - 9 Hole Square Divided by 1 + 9 1 -
160:10 9 Hole Square Divided by 1 + 9 1 - sin so a + b a - b is a² - b² Focusing.
160:17 sin so a + b a - b is a² - b² Focusing. Focusing, paying attention. Now consider the above a - b²
160:22 Focusing, paying attention. Now consider the above a - b² to open. Why so? Now understand what is here
160:24 to open. Why so? Now understand what is here will be? under root above separately so
160:29 will be? under root above separately so 1 - sin theta squared divided by 1 -
160:33 1 - sin theta squared divided by 1 - sin² theta is cos²
160:36 sin² theta is cos² Theta Whole Square. Do you understand what happened?
160:38 Theta Whole Square. Do you understand what happened? Separate in under route numerator. Under Root
160:40 Separate in under route numerator. Under Root Different in the denominator. What was the benefit of that?
160:42 Different in the denominator. What was the benefit of that? Because this is a whole square, it is under the root.
160:44 Because this is a whole square, it is under the root. The square will be cut from it. If this is square then
160:46 The square will be cut from it. If this is square then The square will be cut from the under root. So under
160:48 The square will be cut from the under root. So under The root is gone. What is the only thing left to say?
160:51 The root is gone. What is the only thing left to say? 1 - sin theta / cos theta. Left over 1 - sin
160:56 1 - sin theta / cos theta. Left over 1 - sin theta sitting below cos theta. Now here you are
160:59 theta sitting below cos theta. Now here you are You will learn one more very lovely thing. can I
161:02 You will learn one more very lovely thing. can I Am I here listen am I here 1
161:05 Am I here listen am I here 1 / means cos theta under one different and sin
161:08 / means cos theta under one different and sin I can give cos theta different below theta.
161:11 I can give cos theta different below theta. This is called separating the denominators.
161:14 This is called separating the denominators. What denominator to separate? Now look at
161:16 What denominator to separate? Now look at I can do this, brother, if you
161:18 I can do this, brother, if you If you solve, cos theta common over 1 - sin
161:21 If you solve, cos theta common over 1 - sin theta so I wrote it like this
161:23 theta so I wrote it like this Denominator separated denominator
161:25 Denominator separated denominator I gave it to you separately, now how did your mind work like this?
161:28 I gave it to you separately, now how did your mind work like this? sec theta is 1 / cos theta tan theta
161:32 sec theta is 1 / cos theta tan theta sin / cos theta then 1 / cos theta
161:35 sin / cos theta then 1 / cos theta instead of sec theta sin / cos theta
161:38 instead of sec theta sin / cos theta wrote instead of tan theta hence proved
161:42 wrote instead of tan theta hence proved Left was solving the left hand side
161:44 Left was solving the left hand side I was solving the hand side. Right
161:46 I was solving the hand side. Right The hand side arrived.
161:48 The hand side arrived. Ok? Do you understand? Are you enjoying it?
161:50 Ok? Do you understand? Are you enjoying it? Stay tuned for now. Don't move just yet. Now!
161:54 Stay tuned for now. Don't move just yet. Now! It may not be possible. Don't take tension. will form
161:56 It may not be possible. Don't take tension. will form But okay? Same same ditto same
161:59 But okay? Same same ditto same The question has to be asked in hashtag GPK. Meaning
162:02 The question has to be asked in hashtag GPK. Meaning Have to do it at home. But exactly the same way
162:05 Have to do it at home. But exactly the same way Question. Ok? Come on, a little bit of that type
162:08 Question. Ok? Come on, a little bit of that type Of. Now look what do you want here?
162:10 Of. Now look what do you want here? Square is required and from the right hand side only
162:12 Square is required and from the right hand side only I have to talk. I need square and brother sec
162:16 I have to talk. I need square and brother sec to 1 / cos tan to sin/ cos means sin and
162:19 to 1 / cos tan to sin/ cos means sin and Have to change it to cos. Into sin and cos
162:21 Have to change it to cos. Into sin and cos I have to change it. So divide this side by sin and cos
162:23 I have to change it. So divide this side by sin and cos I have to make a change. in sin then cos already
162:25 I have to make a change. in sin then cos already How will I come in? in sin then cos already
162:28 How will I come in? in sin then cos already How will I come in? When you change sin to cos
162:30 How will I come in? When you change sin to cos You will do it. How is that? And square is also required.
162:33 You will do it. How is that? And square is also required. So what do you do here? again the same
162:35 So what do you do here? again the same thing with LHS raised. Wrote LHS. To all
162:39 thing with LHS raised. Wrote LHS. To all Take this step first. then 1 - sinθ
162:45 Take this step first. then 1 - sinθ 1 + sinθ into what you did above and below yourself
162:49 1 + sinθ into what you did above and below yourself Multiply it? 1 - sin theta and 1 - sin
162:53 Multiply it? 1 - sin theta and 1 - sin Theta. What was the benefit? came up 1 - sin
162:57 Theta. What was the benefit? came up 1 - sin Theta Square.
163:00 Theta Square. came up to 1 - sin theta whole square.
163:02 came up to 1 - sin theta whole square. comes down to 1 - sin² theta. Then 1² - sin²
163:07 comes down to 1 - sin² theta. Then 1² - sin² Theta. Now don't open the square up.
163:10 Theta. Now don't open the square up. Why? Because you should look carefully. 1 -
163:13 Why? Because you should look carefully. 1 - sin theta² is on top and cos² theta is on the bottom.
163:18 sin theta² is on top and cos² theta is on the bottom. So what brother? Square above, square below
163:20 So what brother? Square above, square below Square. So why don't I write it like this?
163:22 Square. So why don't I write it like this? Should I give? 1 - sin theta
163:26 Should I give? 1 - sin theta / cos theta squared. what's the problem
163:28 / cos theta squared. what's the problem This?
163:30 This? You can do this, right? If a² / b² is written
163:34 You can do this, right? If a² / b² is written If so, you can do a / b². Yes and no. So
163:39 If so, you can do a / b². Yes and no. So The square above is the square below, so
163:41 The square above is the square below, so Did it. Now what is the benefit of this?
163:44 Did it. Now what is the benefit of this? I wanted a square and it came. sec theta what
163:46 I wanted a square and it came. sec theta what It happens? What is 1 / cos tan theta?
163:49 It happens? What is 1 / cos tan theta? sin / cos so brother denominator separate one 1
163:53 sin / cos so brother denominator separate one 1 / cos
163:55 / cos - Whole square of sin / cos 1 / cos theta
164:01 - Whole square of sin / cos 1 / cos theta sec theta instead of sin / cos theta
164:05 sec theta instead of sin / cos theta tan theta and this is your whole square which gives you
164:08 tan theta and this is your whole square which gives you I had to bring it, it came sec theta - tan theta hole
164:11 I had to bring it, it came sec theta - tan theta hole Square Hens Proven
164:15 Square Hens Proven Okay, let me ask you a question like this.
164:18 Okay, let me ask you a question like this. There are proven moving people and they will do it
164:21 There are proven moving people and they will do it Don't worry, same thing cosec means 1/
164:24 Don't worry, same thing cosec means 1/ sin cot means cos / sin means below
164:26 sin cot means cos / sin means below sin should go up cos should go down sin should go up
164:29 sin should go up cos should go down sin should go up should cos down should sin up should cos
164:33 should cos down should sin up should cos If you want sin below, that means convert cos to sin
164:36 If you want sin below, that means convert cos to sin We have to change cos to sin
164:38 We have to change cos to sin cos into sin Now which of cos and sin
164:40 cos into sin Now which of cos and sin If the identity is that of a square
164:42 If the identity is that of a square How to get Square How to get Square
164:44 How to get Square How to get Square Same beans to bring you the same cheese squares
164:48 Same beans to bring you the same cheese squares What's the thing, look here, sin theta here, 1-
164:52 What's the thing, look here, sin theta here, 1- cos theta * 1 + cos theta above itself
164:56 cos theta * 1 + cos theta above itself multiply down by 1 + cos theta
164:59 multiply down by 1 + cos theta What was the benefit of multiplying, it came up
165:02 What was the benefit of multiplying, it came up sin theta
165:04 sin theta * 1 + cos theta divided by came down
165:07 * 1 + cos theta divided by came down Your a²
165:09 Your a² - b² advantage is do not open the bracket above so
165:14 - b² advantage is do not open the bracket above so Why Reese's Look at 1 - cos² is sin²
165:20 Why Reese's Look at 1 - cos² is sin² Theta will be subtracted from 1 sin, brother.
165:22 Theta will be subtracted from 1 sin, brother. sin² theta means sinθ * sin theta so one
165:25 sin² theta means sinθ * sin theta so one One sin will be subtracted from sin. 1 + cos / sin
165:29 One sin will be subtracted from sin. 1 + cos / sin How much did you get? 1 + cos theta / sin
165:33 How much did you get? 1 + cos theta / sin What is theta cosec theta? 1 / sin
165:36 What is theta cosec theta? 1 / sin Theta. What is cot theta? cosine
165:38 Theta. What is cot theta? cosine So brother, separate the denominator. under the forest
165:41 So brother, separate the denominator. under the forest sin theta different. sin theta below cos theta
165:46 sin theta different. sin theta below cos theta apart. So what does 1/sin theta become? cosec
165:49 apart. So what does 1/sin theta become? cosec What happened to theta and cos/sin theta? cot
165:52 What happened to theta and cos/sin theta? cot Theta. So cosec theta + cot theta is your answer.
165:55 Theta. So cosec theta + cot theta is your answer. I have arrived. Answer means it has been proved. Haz
165:59 I have arrived. Answer means it has been proved. Haz You will definitely write it as proven. Let's ask cute questions
166:01 You will definitely write it as proven. Let's ask cute questions And a very simple question. ok now here
166:03 And a very simple question. ok now here It is square. Ok? use a little brain
166:05 It is square. Ok? use a little brain Are. What is the right hand side saying?
166:07 Are. What is the right hand side saying? Always start from the right hand side
166:09 Always start from the right hand side Whatever you have to bring. right hand side speaking
166:11 Whatever you have to bring. right hand side speaking That brother change me into cos. me cos
166:12 That brother change me into cos. me cos Change it in. I like it in cos
166:14 Change it in. I like it in cos Is. So basically this is converted into cos, now sin and
166:16 Is. So basically this is converted into cos, now sin and Have to change it to cos. Let's do it. So
166:18 Have to change it to cos. Let's do it. So What is cosec theta? cosec theta
166:21 What is cosec theta? cosec theta You can write 1 /sin theta. cot theta
166:24 You can write 1 /sin theta. cot theta You can write cos theta / sin theta and
166:27 You can write cos theta / sin theta and Here you have made it square. Correct
166:30 Here you have made it square. Correct Is? I am solving the left hand side.
166:33 Is? I am solving the left hand side. First of all, take this step. then now
166:35 First of all, take this step. then now What should I do, friend? What should I do now, friend? this is
166:39 What should I do, friend? What should I do now, friend? this is Buddy
166:46 What do we do now? I have come in cos. not a sin Needed I don't want sin. sin also into cos
166:50 Needed I don't want sin. sin also into cos Have to do it. Do this sin also in cos of father-in-law
166:52 Have to do it. Do this sin also in cos of father-in-law Is. Now to convert sin to cos
166:54 Is. Now to convert sin to cos It needs to be square. So what did I
166:56 It needs to be square. So what did I Did you use your brain? Did I think this through?
166:59 Did you use your brain? Did I think this through? You can write this as 1 - cos
167:02 You can write this as 1 - cos / sin of the whole square. Now Square Inside
167:05 / sin of the whole square. Now Square Inside Give it to me. So there you have it: 1 - cos theta
167:09 Give it to me. So there you have it: 1 - cos theta Square and sin² theta advantage what? 1 -
167:15 Square and sin² theta advantage what? 1 - You get the whole square of cos theta twice 1
167:18 You get the whole square of cos theta twice 1 You can write - cos theta * 1 - cos theta.
167:22 You can write - cos theta * 1 - cos theta. And what is sin² theta? 1
167:25 And what is sin² theta? 1 - cos² theta. If you don't understand, it doesn't matter
167:30 - cos² theta. If you don't understand, it doesn't matter No. I understand one thing, I understand
167:33 No. I understand one thing, I understand What was I asking for cos theta. cos theta
167:36 What was I asking for cos theta. cos theta should be sin theta down here. I
167:38 should be sin theta down here. I What I thought was look at 1 - cos theta
167:42 What I thought was look at 1 - cos theta Square was left written because 1 above -
167:45 Square was left written because 1 above - Need cos theta. Below you wrote this 1 -
167:50 Need cos theta. Below you wrote this 1 - cos² theta sin² theta is equal to 1 - cos² theta.
167:54 cos² theta sin² theta is equal to 1 - cos² theta. Well, if I write one as 1², then someone
167:56 Well, if I write one as 1², then someone No problem, no problem. a² - b² what
168:00 No problem, no problem. a² - b² what It happens? What is a² - b²? Attention
168:04 It happens? What is a² - b²? Attention Give. So a² - b² is a - b a + b so
168:08 Give. So a² - b² is a - b a + b so Now think of it like this: 1 - cos theta times
168:12 Now think of it like this: 1 - cos theta times If it is square, can I write it as 1 - cos
168:15 If it is square, can I write it as 1 - cos Cannot write theta * 1 - cos theta
168:19 Cannot write theta * 1 - cos theta Brother, it's square, meaning twice and below it is a -
168:22 Brother, it's square, meaning twice and below it is a - b * a + b means 1 - cos theta * 1 + cos
168:28 b * a + b means 1 - cos theta * 1 + cos theta Now see what the gain is from 1 - cos 1
168:31 theta Now see what the gain is from 1 - cos 1 - cos went over and came up to 1 - cos theta
168:35 - cos went over and came up to 1 - cos theta It comes down to 1 + cos theta. Good question.
168:38 It comes down to 1 + cos theta. Good question. This was the one you had to prove.
168:42 This was the one you had to prove. Talk to the right hand side or the right hand
168:44 Talk to the right hand side or the right hand What does the right hand side want?
168:46 What does the right hand side want? He is shouting that he is telling me cos
168:48 He is shouting that he is telling me cos If you change in then you have changed in sin cos
168:50 If you change in then you have changed in sin cos Now below is sin so convert sin to cos
168:52 Now below is sin so convert sin to cos If you want to change it then change sin to cos
168:55 If you want to change it then change sin to cos If s is required to be squared then sin must be
168:56 If s is required to be squared then sin must be Given square inside sin² is written as 1 - cos²
169:00 Given square inside sin² is written as 1 - cos² Now I want 1 + cos² then 1 - cos²
169:03 Now I want 1 + cos² then 1 - cos² I wrote a- - b * a + b and it worked for me. Correct
169:07 I wrote a- - b * a + b and it worked for me. Correct Is? Just keep watching the next one. what to say next
169:09 Is? Just keep watching the next one. what to say next Used to be? Nice clean right hand side
169:11 Used to be? Nice clean right hand side What are you saying? Very easy question. Right
169:13 What are you saying? Very easy question. Right What is the hand side saying? the child to whom
169:16 What is the hand side saying? the child to whom I don't understand trigonometry at all.
169:19 I don't understand trigonometry at all. I will say just one thing. Identities A Paper
169:22 I will say just one thing. Identities A Paper Write it in me. and keep those identities in your
169:25 Write it in me. and keep those identities in your Sit in front. When you are asking questions
169:27 Sit in front. When you are asking questions yes. Oh, that rotten reciprocal identity
169:30 yes. Oh, that rotten reciprocal identity Is. It is an identity with a content. Forest and
169:32 Is. It is an identity with a content. Forest and It has a square identity. rotten
169:34 It has a square identity. rotten These are basic identities. Ok? And
169:37 These are basic identities. Ok? And Start with this question.
169:39 Start with this question. The right hand side is shouting
169:41 The right hand side is shouting Let me convert it to sin cos. me sin
169:43 Let me convert it to sin cos. me sin Change it to cos. me in sin cos
169:45 Change it to cos. me in sin cos Change it. So do it. Simple. so what friend
169:47 Change it. So do it. Simple. so what friend Can cot be converted to sin cos?
169:50 Can cot be converted to sin cos? Absolutely. This is the first step you should take to cot.
169:54 Absolutely. This is the first step you should take to cot. You can write cot in the second step.
169:57 You can write cot in the second step. You can write cosθ / sinθ tan as sinθ /
170:03 You can write cosθ / sinθ tan as sinθ / keep watching cos theta what to do now what now
170:06 keep watching cos theta what to do now what now The thing to do is to take the LCM of sin theta
170:08 The thing to do is to take the LCM of sin theta LCM of cos theta is sinθ cos theta above
170:13 LCM of cos theta is sinθ cos theta above what will come here sin here sin
170:15 what will come here sin here sin sin here sin here what's left cos so
170:17 sin here sin here what's left cos so cos * cos cos * cos cos² here cos
170:22 cos * cos cos * cos cos² here cos cos left over here sin over here cos over here
170:25 cos left over here sin over here cos over here cos left sin sin so sin goes up
170:27 cos left sin sin so sin goes up multiply sin * sin sin theta sorry sin²
170:31 multiply sin * sin sin theta sorry sin² theta so sin theta cos theta so come down
170:35 theta so sin theta cos theta so come down sin theta cos theta came down so now it's up
170:38 sin theta cos theta came down so now it's up what do you need just cos what do you need
170:40 what do you need just cos what do you need I only have cos so cos and sin are above
170:43 I only have cos so cos and sin are above What do I need, only cos, I have cos and
170:45 What do I need, only cos, I have cos and If it is a sin, then this sin will have to be removed, brother.
170:49 If it is a sin, then this sin will have to be removed, brother. If you don't want sin then don't want this sin
170:51 If you don't want sin then don't want this sin I will have to remove it brother, what is there up here?
170:54 I will have to remove it brother, what is there up here? which is not here sin so this sin sin
170:56 which is not here sin so this sin sin Will have to remove it. Now change sin to what?
170:59 Will have to remove it. Now change sin to what? should I? in cos because we need cos above.
171:02 should I? in cos because we need cos above. Can sin be converted to cos?
171:05 Can sin be converted to cos? Absolutely put a minus. Write sin² instead of sin²
171:09 Absolutely put a minus. Write sin² instead of sin² Given 1 - cos² theta identity. don't cram
171:14 Given 1 - cos² theta identity. don't cram Is. If you memorize it, it will never be done. sin²
171:18 Is. If you memorize it, it will never be done. sin² Write 1 - cos² and put brackets. Now enough
171:22 Write 1 - cos² and put brackets. Now enough Open the bracket. The answer will come. So here
171:24 Open the bracket. The answer will come. So here your cos² theta minus went in so
171:28 your cos² theta minus went in so -1 minus went in so plus cos² theta
171:35 -1 minus went in so plus cos² theta Okay, and here you go, sin theta * cos
171:40 Okay, and here you go, sin theta * cos theta is simply cos² + cos²
171:44 theta is simply cos² + cos² 2 cos² theta - 1
171:48 2 cos² theta - 1 / sin theta * cos theta exactly
171:52 / sin theta * cos theta exactly Lallu Question
171:59 Ok? Easy. Ok. Now I think I am gaining some confidence gradually. Ok
172:01 I am gaining some confidence gradually. Ok No? Take a break and watch the entire lecture.
172:04 No? Take a break and watch the entire lecture. Please do watch it. Please do watch it. Ok? I
172:07 Please do watch it. Please do watch it. Ok? I You should practice so many questions.
172:09 You should practice so many questions. I will tell you that you cannot imagine. probably by myself
172:11 I will tell you that you cannot imagine. probably by myself I will have to do something. Ok? Let go. So friend
172:15 I will have to do something. Ok? Let go. So friend What did I say? things in sin cos
172:17 What did I say? things in sin cos Think about it. Now sec means 1 / cos, sec means
172:20 Think about it. Now sec means 1 / cos, sec means 1 / cos ok. Yes, so cos have to be brought. cos
172:24 1 / cos ok. Yes, so cos have to be brought. cos Have to bring it. Ok? So change this to cos
172:26 Have to bring it. Ok? So change this to cos have to do it. Now this is already in sin
172:28 have to do it. Now this is already in sin Is. Perhaps sin can also be converted to cos
172:31 Is. Perhaps sin can also be converted to cos Can. The basic sin is cos. Basic
172:33 Can. The basic sin is cos. Basic sin is cos. Ok? So tan theta
172:35 sin is cos. Ok? So tan theta Can I change it to sin cos?
172:37 Can I change it to sin cos? Absolutely. So do it, the answer will come immediately.
172:39 Absolutely. So do it, the answer will come immediately. Just look. left hand side tan theta
172:42 Just look. left hand side tan theta wrote. tan theta is written as sin theta / cos theta
172:45 wrote. tan theta is written as sin theta / cos theta Theta. Your plus here
172:49 Theta. Your plus here What is written here, boss? sinθ
172:54 What is written here, boss? sinθ / cos theta What is written here? of the minus
172:58 / cos theta What is written here? of the minus sin theta. Now here's something that
173:01 sin theta. Now here's something that But it is not. Which you had to bring cos here.
173:04 But it is not. Which you had to bring cos here. Have to change it to cos. So cos is then
173:06 Have to change it to cos. So cos is then There is also sin. If you use your brain a little.
173:10 There is also sin. If you use your brain a little. One term these one term these both have sin
173:13 One term these one term these both have sin Is. Called out that sin. Left inside 1/
173:18 Is. Called out that sin. Left inside 1/ cos theta + 1 how bro? If from here sin
173:22 cos theta + 1 how bro? If from here sin went to 1 / cos theta. If sin goes from here then
173:26 went to 1 / cos theta. If sin goes from here then 1 hole divided by if either of these
173:29 1 hole divided by if either of these If I take out sin theta, here
173:32 If I take out sin theta, here will be left at 1 / cos theta. Here, the remainder is -1
173:37 will be left at 1 / cos theta. Here, the remainder is -1 sin theta to sin theta divided by 1 / cos theta
173:40 sin theta to sin theta divided by 1 / cos theta sec theta is 1 / cos theta
173:46 sec theta is 1 / cos theta sec theta + 1 - 1
173:50 sec theta + 1 - 1 This is what you had to bring, Hans Proved
173:55 This is what you had to bring, Hans Proved Easy, okay, let's move ahead, what are you saying next?
173:59 Easy, okay, let's move ahead, what are you saying next? Okay, now this is a good question here.
174:01 Okay, now this is a good question here. What are you saying here again here
174:04 What are you saying here again here But what are you saying to a lot of children?
174:05 But what are you saying to a lot of children? Seeing this for the first time, it seems that this
174:07 Seeing this for the first time, it seems that this So it is a wrong question. cosec² theta + sec² theta
174:10 So it is a wrong question. cosec² theta + sec² theta to cosec² theta * sec² theta
174:13 to cosec² theta * sec² theta Is. How will they do this? The question was wrong, man.
174:16 Is. How will they do this? The question was wrong, man. This is not it, you are understanding two ratios
174:19 This is not it, you are understanding two ratios Written in multiples. them to you
174:21 Written in multiples. them to you To bring in multiplication. How will you get this
174:24 To bring in multiplication. How will you get this Buddy? What did I say? things in sin cos
174:27 Buddy? What did I say? things in sin cos Think about it. thought things out in sin cos
174:29 Think about it. thought things out in sin cos do it. Because each trigonometric ratio
174:31 do it. Because each trigonometric ratio There is a change in sin cos. Ok?
174:33 There is a change in sin cos. Ok? If you are thinking in sin cos then sin cos
174:34 If you are thinking in sin cos then sin cos Boss so I can write to cosec²
174:37 Boss so I can write to cosec² I can write 1 / sin² sec² as 1
174:42 I can write 1 / sin² sec² as 1 / cos² Even if I don't understand anything, this much
174:45 / cos² Even if I don't understand anything, this much So one must know who is in what
174:47 So one must know who is in what You can change it.
174:49 You can change it. Ok? In the same old page you
174:52 Ok? In the same old page you I will take it back. You already know this
174:56 I will take it back. You already know this Should be. This should be known. Some?
175:00 Should be. This should be known. Some? It should also happen that brother sin theta in reciprocal
175:03 It should also happen that brother sin theta in reciprocal cos theta sec theta with cosec theta
175:05 cos theta sec theta with cosec theta in reciprocal along tan theta cot theta
175:08 in reciprocal along tan theta cot theta In reciprocal together means where tan
175:10 In reciprocal together means where tan If you write theta, you can replace it with 1 / cot theta
175:13 If you write theta, you can replace it with 1 / cot theta where cot theta is written
175:14 where cot theta is written replace 1 / tan theta somewhere tan² theta
175:18 replace 1 / tan theta somewhere tan² theta If it is written then you can write it as 1 / cot² theta somewhere
175:20 If it is written then you can write it as 1 / cot² theta somewhere cot theta is written, instead you can write 1 /
175:23 cot theta is written, instead you can write 1 / tan² theta do you understand what I am saying
175:26 tan² theta do you understand what I am saying If it is written somewhere sec theta then
175:28 If it is written somewhere sec theta then instead of 1 / cos theta you guys get the
175:31 instead of 1 / cos theta you guys get the Points and these basic things you should know
175:33 Points and these basic things you should know Only then will you be able to ask these questions. Anyway
175:37 Only then will you be able to ask these questions. Anyway Let's continue, boss is there, so let's go.
175:40 Let's continue, boss is there, so let's go. So I changed it to sin cos. Now what
175:42 So I changed it to sin cos. Now what should I? Now I am not able to understand anything.
175:44 should I? Now I am not able to understand anything. I can't understand anything. So basic maths basic
175:47 I can't understand anything. So basic maths basic Maths means taking LCM of something. So
175:51 Maths means taking LCM of something. So What is the LCM of sin² cos²? sin²
175:55 What is the LCM of sin² cos²? sin² theta * cos² theta. What above? sin² sin²
175:59 theta * cos² theta. What above? sin² sin² sin² sin² What is left? So put it up
176:01 sin² sin² What is left? So put it up multiply then cos² * 1 cos² theta cos²
176:04 multiply then cos² * 1 cos² theta cos² cos² cos² cos² this is left so put it on top
176:07 cos² cos² cos² this is left so put it on top Multiply then sin² * 1 is sin² theta. Now
176:11 Multiply then sin² * 1 is sin² theta. Now One thing is useful. cos² + sin² is 1.
176:15 One thing is useful. cos² + sin² is 1. So it comes down to 1 / sin² theta * cos² theta.
176:20 So it comes down to 1 / sin² theta * cos² theta. Now tell me one thing. What above I 1 * 1
176:24 Now tell me one thing. What above I 1 * 1 Can I write it myself? The forest was already there. into
176:26 Can I write it myself? The forest was already there. into 1 did it myself. What is 1 / sin²?
176:30 1 did it myself. What is 1 / sin²? What is 1 / cos²? is 1 / sin²
176:34 What is 1 / cos²? is 1 / sin² cosec² theta. 1 / cos² is sec² theta.
176:40 cosec² theta. 1 / cos² is sec² theta. cosec² theta * sec² theta is the answer
176:43 cosec² theta * sec² theta is the answer You had to bring it.
176:47 You had to bring it. Keep watching, keep watching. Don't go now. Now!
176:50 Keep watching, keep watching. Don't go now. Now! 15 questions have not been done. Okay, right?
176:52 15 questions have not been done. Okay, right? Patience. Let us go. What do you want to bring, boss? bringing you
176:55 Patience. Let us go. What do you want to bring, boss? bringing you There is forest. To bring a good forest means all
176:57 There is forest. To bring a good forest means all Trigonometric ratios are canceling out
176:59 Trigonometric ratios are canceling out Will be. Ok? The basic sin cos is the same. But
177:02 Will be. Ok? The basic sin cos is the same. But Let's take a look once again. So cosec sin
177:05 Let's take a look once again. So cosec sin sec cos tan cot brother six of six
177:08 sec cos tan cot brother six of six Gave the ratios. If you are doing something like this
177:10 Gave the ratios. If you are doing something like this If yes then change it to sin cos, the work is easy.
177:12 If yes then change it to sin cos, the work is easy. It happens. So I wrote cosec as 1/
177:15 It happens. So I wrote cosec as 1/ sin Here sin is already written. Now
177:18 sin Here sin is already written. Now I'll use the short form a little bit because
177:19 I'll use the short form a little bit because I want to save you some time. Oho
177:22 I want to save you some time. Oho Don't do this in the exam. in the exam
177:24 Don't do this in the exam. in the exam Do it completely now because I want you
177:26 Do it completely now because I want you I want to practice most of the questions
177:28 I want to practice most of the questions I am doing the short form so that I can get it done.
177:30 I am doing the short form so that I can get it done. You will understand. I Guess Starting In
177:31 You will understand. I Guess Starting In I did not do it because I was not comfortable. But now
177:34 I did not do it because I was not comfortable. But now You will become comfortable. 1 / cos sec
177:37 You will become comfortable. 1 / cos sec cos of cos here c means cos of s
177:40 cos of cos here c means cos of s Meaning sin is okay, right? tan sin / cos cot
177:44 Meaning sin is okay, right? tan sin / cos cot Basic changes to cos/sin are inevitable.
177:47 Basic changes to cos/sin are inevitable. Needed What is written here? Left Hand
177:50 Needed What is written here? Left Hand Side. Ok? Now what will you do now? in sin cos
177:53 Side. Ok? Now what will you do now? in sin cos So the change happened. LCM to LCM Basic
177:56 So the change happened. LCM to LCM Basic Doing basic maths. If you are here
177:58 Doing basic maths. If you are here Will you take LCM, okay? So sin and one
178:01 Will you take LCM, okay? So sin and one LCM sin here sin here sin so
178:04 LCM sin here sin here sin so One above as it is here one here sin
178:06 One above as it is here one here sin One here, sin one here, one here
178:08 One here, sin one here, one here What should I multiply by in pe sin one? sin
178:11 What should I multiply by in pe sin one? sin sin then sin * sin sin² or direct
178:13 sin then sin * sin sin² or direct You can do it like this also. If there is a forest here,
178:16 You can do it like this also. If there is a forest here, If you multiply this directly here then it will be 1
178:18 If you multiply this directly here then it will be 1 - sin² / sin What will come here? 1 -
178:23 - sin² / sin What will come here? 1 - cos² / cos What does cos and sin mean here?
178:26 cos² / cos What does cos and sin mean here? LCM cosin cos cos cos cos left sin then
178:30 LCM cosin cos cos cos cos left sin then sin * sin sin² sin sin sin sin save cos
178:33 sin * sin sin² sin sin sin sin save cos So cos * cos cos²
178:36 So cos * cos cos² Okay, keep doing it and see what you get.
178:39 Okay, keep doing it and see what you get. goes? cos² is 1 - sin² cos²
178:42 goes? cos² is 1 - sin² cos² sin 1 - cos² below sin² below cos
178:46 sin 1 - cos² below sin² below cos sin² + cos² is 1 and below cos sin is now
178:49 sin² + cos² is 1 and below cos sin is now You probably understood it came up as cos² * sin²
178:53 You probably understood it came up as cos² * sin² came down to sin * sin sin² cos * cos cos²
178:58 came down to sin * sin sin² cos * cos cos² It's all in the multiplication. So cos²
179:00 It's all in the multiplication. So cos² cos² went. sin² went from sin² to sin². Not Zero
179:03 cos² went. sin² went from sin² to sin². Not Zero The forest is saved.
179:06 The forest is saved. Okay, right? All right. Did you understand here?
179:09 Okay, right? All right. Did you understand here? What brother? sin * cos * cos * sin then sin *
179:12 What brother? sin * cos * cos * sin then sin * sin sin² cos * cos cos²
179:16 sin sin² cos * cos cos² EG take another look cute question what are you saying
179:20 EG take another look cute question what are you saying Are? Again you have to bring two. lots of t
179:24 Are? Again you have to bring two. lots of t Ratios are given. to convert to sin cos
179:26 Ratios are given. to convert to sin cos What should I look at? So brother one left hand side
179:31 What should I look at? So brother one left hand side pay attention. 1 + cot is written as cos/sin
179:35 pay attention. 1 + cot is written as cos/sin cosec wrote 1 /sin keep watching comfortably
179:39 cosec wrote 1 /sin keep watching comfortably 1 + tan written as sin / cos sec written as 1
179:43 1 + tan written as sin / cos sec written as 1 / cos okay plant a forest under it
179:48 / cos okay plant a forest under it put a forest down okay forest of sin sin
179:51 put a forest down okay forest of sin sin LCM sin will come here one here
179:54 LCM sin will come here one here sin so sin over sin 1 sin over here sin
179:57 sin so sin over sin 1 sin over here sin sin over here so cos over here sin over here
179:59 sin over here so cos over here sin over here Pay sin up one as it is
180:02 Pay sin up one as it is 1 cos and cos cos LCM cos now one thing
180:05 1 cos and cos cos LCM cos now one thing So it makes sense if here cos here
180:07 So it makes sense if here cos here cos LCM is also cos so sin + 1 over here
180:10 cos LCM is also cos so sin + 1 over here It is here what will come in the forest
180:12 It is here what will come in the forest If I multiply cos cos then cos * 1 cos comes
180:15 If I multiply cos cos then cos * 1 cos comes It has come like this
180:17 It has come like this What should I do now, I don't understand anything.
180:18 What should I do now, I don't understand anything. As for sin cos, I changed the basic
180:21 As for sin cos, I changed the basic Maths, what will you do now? Open the brackets.
180:23 Maths, what will you do now? Open the brackets. This sin goes into all three and then this cos
180:26 This sin goes into all three and then this cos Going into the three and then going into the minus
180:28 Going into the three and then going into the minus Of the three, first sin goes and then cos cos
180:31 Of the three, first sin goes and then cos cos I am sin cos sin and I am sin *
180:34 I am sin cos sin and I am sin * sin sin² sin if you go to the forest then this is your sin
180:38 sin sin² sin if you go to the forest then this is your sin cos² cos² sin
180:42 cos² cos² sin If I go to the forest then cosin cos = cos -1
180:46 If I go to the forest then cosin cos = cos -1 going to cos then - cos -1 going to sin then
180:50 going to cos then - cos -1 going to sin then -sin -1 going one then -1 hole divided
180:54 -sin -1 going one then -1 hole divided Bye down your sin * cos sin cos something
180:58 Bye down your sin * cos sin cos something Is there any benefit? Is there any benefit?
181:00 Is there any benefit? Is there any benefit? What are you looking at, I hope I don't make any mistake
181:04 What are you looking at, I hope I don't make any mistake Didi, I don't see anything wrong yet, come on.
181:08 Didi, I don't see anything wrong yet, come on. Anyway, this is yours if you pay attention plus
181:11 Anyway, this is yours if you pay attention plus sin of to -sin of plus cos of to - cos
181:15 sin of to -sin of plus cos of to - cos What is left is sin cos + sin cos so this
181:19 What is left is sin cos + sin cos so this Your 2sin cos then this is your look sin² left
181:23 Your 2sin cos then this is your look sin² left So sin² is written down, cos² is left, so write cos²
181:27 So sin² is written down, cos² is left, so write cos² taken here pay -1 left divided divided by
181:30 taken here pay -1 left divided divided by What's the point of sin cos? sin² + cos² sin² +
181:35 What's the point of sin cos? sin² + cos² sin² + cos² 1 So what did you get? 2sin cos
181:39 cos² 1 So what did you get? 2sin cos It was already there. Instead, 1 - 1 down from the first
181:44 It was already there. Instead, 1 - 1 down from the first sin cos goes from + 1 to -1 so 2sin cos / sin
181:49 sin cos goes from + 1 to -1 so 2sin cos / sin cos sin to sin cos to cos to left. Which is
181:53 cos sin to sin cos to cos to left. Which is You have to bring it.
181:56 You have to bring it. Ok?
181:57 Ok? Let me repeat it once again. this one
181:59 Let me repeat it once again. this one I have done basic maths. from the short form
182:03 I have done basic maths. from the short form Please don't panic. Don't do CS in the exam
182:05 Please don't panic. Don't do CS in the exam Write You have to write everything completely in the exam.
182:07 Write You have to write everything completely in the exam. cos / sin 1 /sin sin / cos 1 / cos OK
182:12 cos / sin 1 /sin sin / cos 1 / cos OK Is? So what will be the LCM of all three brother?
182:14 Is? So what will be the LCM of all three brother? The LCM of 1 2 and 2 will be two. so just like that
182:17 The LCM of 1 2 and 2 will be two. so just like that One sin and the LCM of sin is sin. Correct
182:19 One sin and the LCM of sin is sin. Correct Is? One here sin here so sin up
182:22 Is? One here sin here so sin up two sin * 1 sin sin sin sin so up as it
182:25 two sin * 1 sin sin sin sin so up as it is cos - 1 cos cos cos so up as it is
182:29 is cos - 1 cos cos cos so up as it is sin + 1. That's it, you have your cos here. Then
182:32 sin + 1. That's it, you have your cos here. Then This one sin go into this into this into this
182:35 This one sin go into this into this into this gonna cos go into this into this into this -1
182:39 gonna cos go into this into this into this -1 Something like this came into this.
182:41 Something like this came into this. sin cos + sin cos 2sin cos sin² + cos²
182:46 sin cos + sin cos 2sin cos sin² + cos² separately and -1 separately because -sin + sin +
182:51 separately and -1 separately because -sin + sin + cos - cos cut off. sin² + cos² is 1.
182:56 cos - cos cut off. sin² + cos² is 1. So +1 became -1. 2sin cos s / sin cos s
182:59 So +1 became -1. 2sin cos s / sin cos s cos sin cos gone to saved. Ok? Let us go
183:04 cos sin cos gone to saved. Ok? Let us go Next. Very nice question. CBSE's
183:07 Next. Very nice question. CBSE's One of the most favorite questions
183:10 One of the most favorite questions The hashtag is very easy but say cute.
183:13 The hashtag is very easy but say cute. This. Ok? And you know this is it
183:16 This. Ok? And you know this is it type of question given by CBSE this year
183:18 type of question given by CBSE this year Was. This is a question from your NCERT. And you
183:21 Was. This is a question from your NCERT. And you See what kind of questions CBSE has asked this year.
183:24 See what kind of questions CBSE has asked this year. I had asked. Let's ask this question first. Correct
183:25 I had asked. Let's ask this question first. Correct Is? Now, friend, you have to find tan theta. I
183:28 Is? Now, friend, you have to find tan theta. I what did you say? Think in sin cos. Ok?
183:30 what did you say? Think in sin cos. Ok? So tan theta means sin / cos well
183:34 So tan theta means sin / cos well Need sin above. Need cos below. Ok?
183:36 Need sin above. Need cos below. Ok? Let's use our brains. So sin and cos are there.
183:38 Let's use our brains. So sin and cos are there. Sin and cos are there. already in sin cos
183:41 Sin and cos are there. already in sin cos This means basic simplification will have to be done.
183:43 This means basic simplification will have to be done. Friend, first of all what should I do in sin cos
183:46 Friend, first of all what should I do in sin cos What should I do first of all, understand one thing?
183:50 What should I do first of all, understand one thing? First of all, if you look up
183:54 First of all, if you look up one sin next to it three times sin so
183:57 one sin next to it three times sin so If you look above, sin theta once common
184:01 If you look above, sin theta once common can be removed and the forest left here above
184:03 can be removed and the forest left here above The remainder here is 2 sin² theta divided by
184:09 The remainder here is 2 sin² theta divided by here here cos here cos so if you
184:11 here here cos here cos so if you Take out cos theta common carefully so here
184:16 Take out cos theta common carefully so here at 2 cos²
184:18 at 2 cos² theta over here is -1 so why cos theta * this
184:22 theta over here is -1 so why cos theta * this 2 cos theta cos theta * -1 - cos theta now
184:26 2 cos theta cos theta * -1 - cos theta now Look, sinθ / cos theta is tan theta.
184:31 Look, sinθ / cos theta is tan theta. So you have understood sin/cos brother, now you have understood sin/
184:34 So you have understood sin/cos brother, now you have understood sin/ You wanted cos, not sin/cos
184:36 You wanted cos, not sin/cos sin / cos already comes, which means
184:40 sin / cos already comes, which means What might be happening, brother, this is obvious.
184:44 What might be happening, brother, this is obvious. The thing is it must be cutting. I will say it again
184:47 The thing is it must be cutting. I will say it again What you needed has already arrived. Who
184:50 What you needed has already arrived. Who You should have come after taking out the common
184:52 You should have come after taking out the common Went. Meaning, these remaining things are being cut.
184:54 Went. Meaning, these remaining things are being cut. Will happen. When do things get cut off? When there are beans.
184:58 Will happen. When do things get cut off? When there are beans. So either convert sin to cos or
185:01 So either convert sin to cos or So cos into sin. any one thing that
185:04 So cos into sin. any one thing that Your wish. So here I wrote
185:06 Your wish. So here I wrote sin theta / cos theta. Pay attention everyone.
185:10 sin theta / cos theta. Pay attention everyone. Ok? Watch comfortably. Ok? so so so
185:13 Ok? Watch comfortably. Ok? so so so so so so so
185:16 so so so so 1 - Do brackets. 1 - 2 sin² to cos²
185:22 1 - Do brackets. 1 - 2 sin² to cos² To write sin² in s I divided it by 1 - cos²
185:26 To write sin² in s I divided it by 1 - cos² Wrote it. Ok? And what's left below? Below
185:29 Wrote it. Ok? And what's left below? Below as it is 2 cos²
185:32 as it is 2 cos² Theta - I am saying it once again
185:34 Theta - I am saying it once again What did you do? Change sin² to cos². So up
185:37 What did you do? Change sin² to cos². So up I wrote sin² as 1 - cos²
185:40 I wrote sin² as 1 - cos² What was the benefit of this? Let sinθ /
185:43 What was the benefit of this? Let sinθ / cosθ do one thing. Write tan theta itself
185:46 cosθ do one thing. Write tan theta itself I give. If you look inside, then 1-2 go into the forest.
185:49 I give. If you look inside, then 1-2 go into the forest. So -2 goes into cos² plus 2.
185:54 So -2 goes into cos² plus 2. cos² theta and down to your 2 cos² theta - 1
186:00 cos² theta and down to your 2 cos² theta - 1 Now let's see what happens. So here you come
186:04 Now let's see what happens. So here you come tanθ
186:06 tanθ 1 - 2 1 - 2 -1 1 - 2 - 1 So here it is
186:11 1 - 2 1 - 2 -1 1 - 2 - 1 So here it is your 2 cos² theta 2 cos² theta and 1 - 2 -
186:18 your 2 cos² theta 2 cos² theta and 1 - 2 - 1
186:20 1 - 1 and even lower if you look, 2 cos²
186:24 - 1 and even lower if you look, 2 cos² Theta - 1 you understand I started with
186:28 Theta - 1 you understand I started with What did you think that if I sinned from above
186:30 What did you think that if I sinned from above If cos cos is taken out from below then sin / cos tan
186:33 If cos cos is taken out from below then sin / cos tan Theta came automatically. means the inside
186:35 Theta came automatically. means the inside Things might be getting removed, cancelled.
186:37 Things might be getting removed, cancelled. When things get cancelled when they are the same
186:39 When things get cancelled when they are the same Are. So the sin² above I wrote as 1 -
186:42 Are. So the sin² above I wrote as 1 - By doing this cos² the top and bottom are exactly the same. So
186:47 By doing this cos² the top and bottom are exactly the same. So Don't do this, 2 to 2 or c to c
186:50 Don't do this, 2 to 2 or c to c o to o these s to s² 2 to 2 theta to theta
186:54 o to o these s to s² 2 to 2 theta to theta Minus to minus one doesn't equal one.
186:56 Minus to minus one doesn't equal one. Is. Isn't it? It should not be cut like this. not like that
186:59 Is. Isn't it? It should not be cut like this. not like that You guys do it. Yes. Come on brother, complete it
187:03 You guys do it. Yes. Come on brother, complete it Will be cut from. Ok? So look at your tan theta
187:07 Will be cut from. Ok? So look at your tan theta You got the answer you wanted.
187:11 You got the answer you wanted. Ok? This is a NCERT question. Now this
187:13 Ok? This is a NCERT question. Now this See what questions are there in the 2025 paper.
187:17 See what questions are there in the 2025 paper. CBSE had asked. CBSE 2025
187:20 CBSE had asked. CBSE 2025 Question. We think what can you ask friend
187:23 Question. We think what can you ask friend Took. The paper came from outside. Doesn't happen like this.
187:26 Took. The paper came from outside. Doesn't happen like this. He just gives it a slight twist. Little
187:28 He just gives it a slight twist. Little I will ask you to use your brain also.
187:30 I will ask you to use your brain also. If you give it directly then it will not be fun, friend.
187:32 If you give it directly then it will not be fun, friend. Ok? Look, the exact same question.
187:34 Ok? Look, the exact same question. Is. It is exactly the same question. you think
187:37 Is. It is exactly the same question. you think Look at this. If you look at the cos common from above here
187:42 Look at this. If you look at the cos common from above here You will take it out. I am just explaining directly
187:44 You will take it out. I am just explaining directly Am. If you take out sin common from below then cos /
187:46 Am. If you take out sin common from below then cos / What will sin become?
187:49 What will sin become? cot will be made. And inside you know, inside you
187:53 cot will be made. And inside you know, inside you Whatever comes in above 1 - 2 cos²
187:57 Whatever comes in above 1 - 2 cos² Your 1 - 2 below
188:01 Your 1 - 2 below sin²
188:03 sin² Ok? This will not be cut completely. Once
188:06 Ok? This will not be cut completely. Once I'm telling you again what I want to say
188:08 I'm telling you again what I want to say I have been. cos from above and sin from below
188:11 I have been. cos from above and sin from below Common is cos / sin cos / sin cot and
188:14 Common is cos / sin cos / sin cot and This will be completely cut. you look like
188:17 This will be completely cut. you look like Like it was cut here. Like the cut here
188:19 Like it was cut here. Like the cut here Had gone.
188:21 Had gone. Ok? Well, the things inside here too
188:24 Ok? Well, the things inside here too Will be cut. How? You look at it like this. 1 - 2
188:27 Will be cut. How? You look at it like this. 1 - 2 Write 1 instead of cos² -
188:30 Write 1 instead of cos² - sin²
188:32 sin² Ok? Any problem? Now yours has come up
188:34 Ok? Any problem? Now yours has come up 1 - 2 + 2sin² 1 - 2 + 2sin² Your answer below
188:39 1 - 2 + 2sin² 1 - 2 + 2sin² Your answer below Gaya 1 -
188:41 Gaya 1 - 2sin²
188:43 2sin² Ok? Focusing with complete ease
188:45 Ok? Focusing with complete ease to do. Focusing focus. Ok? So up
188:48 to do. Focusing focus. Ok? So up Have you arrived? If you pay attention. came up -1
188:53 Have you arrived? If you pay attention. came up -1 + 2sin² -1 + 2sin² down to 1 - 2sin²
188:59 + 2sin² -1 + 2sin² down to 1 - 2sin² Ok? Now you will say friend, this is cut.
189:01 Ok? Now you will say friend, this is cut. No more. Break down.
189:03 No more. Break down. up -1 down +1 up + 2sin² down - 2sin²
189:08 up -1 down +1 up + 2sin² down - 2sin² If you are here I am discussing.
189:10 If you are here I am discussing. If you take out the minus sign common here
189:12 If you take out the minus sign common here So this is your +1 and this is your - 2sin²
189:17 So this is your +1 and this is your - 2sin² And the same thing below -
189:20 And the same thing below - 2sin² is then 1 - 2sin² 1 - 2sin² cut off. Bus
189:24 2sin² is then 1 - 2sin² 1 - 2sin² cut off. Bus He gave out a minus sign. These
189:26 He gave out a minus sign. These minus you put it here which is -cot theta
189:29 minus you put it here which is -cot theta - cot theta + cot theta 0
189:34 - cot theta + cot theta 0 Did you understand or not? Did you understand or not?
189:39 Did you understand or not? Did you understand or not? cos common from above sin common cos from below /
189:42 cos common from above sin common cos from below / sin cot theta arrived. Now cot theta + cot
189:46 sin cot theta arrived. Now cot theta + cot Theta will not be zero. 2 cot theta will come.
189:48 Theta will not be zero. 2 cot theta will come. So there's a minus sign somewhere here.
189:51 So there's a minus sign somewhere here. Needed So how come there is a minus sign here?
189:53 Needed So how come there is a minus sign here? Came? It came from inside. You understand here
189:56 Came? It came from inside. You understand here Here the inside things were cut directly.
189:59 Here the inside things were cut directly. Was. And in this question, the things inside
190:03 Was. And in this question, the things inside Only then did I remove the common minus sign from
190:05 Only then did I remove the common minus sign from Cut. And with the help of that minus sign, this
190:08 Cut. And with the help of that minus sign, this -cot theta. -cot theta + cot theta 0
190:12 -cot theta. -cot theta + cot theta 0 NCERT question of the year.
190:16 NCERT question of the year. Ok? Tell me when I give you this
190:19 Ok? Tell me when I give you this I am getting the year's questions done. If you
190:20 I am getting the year's questions done. If you You are still watching the video, properly
190:22 You are still watching the video, properly Are you watching, sincerely watching, what
190:24 Are you watching, sincerely watching, what Are you getting help? do you
190:26 Are you getting help? do you I understand what kind of CBSE
190:28 I understand what kind of CBSE Papers starting to make now? slightly
190:31 Papers starting to make now? slightly He just twists it. wants you to
190:33 He just twists it. wants you to Use your brain a little. Next question, another one
190:35 Use your brain a little. Next question, another one Just look. Ok? These are yours, these are yours
190:38 Just look. Ok? These are yours, these are yours This is a question of NCERT. A lot of NCERT
190:41 This is a question of NCERT. A lot of NCERT Easy question. What questions did CBSE ask? You
190:43 Easy question. What questions did CBSE ask? You Look First they would ask NCERT questions.
190:45 Look First they would ask NCERT questions. Are. Ok? What are you saying? sin theta
190:47 Are. Ok? What are you saying? sin theta + cosec theta whole square cos theta + sec
190:50 + cosec theta whole square cos theta + sec theta whole square tan² + cot² I did
190:53 theta whole square tan² + cot² I did spoke? Think of things in terms of sin cos.
190:54 spoke? Think of things in terms of sin cos. But please use your brain a little bit, friend.
190:59 But please use your brain a little bit, friend. First, if you divide it here into 1 / sin
191:01 First, if you divide it here into 1 / sin Listening to convert. You can convert this to 1/sin
191:03 Listening to convert. You can convert this to 1/sin Convert it. Then open the hole square.
191:07 Convert it. Then open the hole square. Write this as 1 / cos. Then the hole square
191:09 Write this as 1 / cos. Then the hole square Open it. You can do it that way also.
191:13 Open it. You can do it that way also. Ok? But do you know an easier way?
191:15 Ok? But do you know an easier way? will be? I tell you. If you hole square
191:18 will be? I tell you. If you hole square When you open it, use your brain a little. If you hole
191:21 When you open it, use your brain a little. If you hole If you open the square, a + b²
191:24 If you open the square, a + b² So cosec squared will come out to be. cosec
191:26 So cosec squared will come out to be. cosec square will come and you can convert cosec² to cot²
191:30 square will come and you can convert cosec² to cot² You can change it.
191:32 You can change it. If you change it here without sin cos
191:35 If you change it here without sin cos Meaning, without converting it into cos
191:38 Meaning, without converting it into cos If you open the square, this is the square of sec
191:40 If you open the square, this is the square of sec will come and you can convert sec² into tan²
191:43 will come and you can convert sec² into tan² Are. There is identity. Understanding the meaning of cosec²
191:48 Are. There is identity. Understanding the meaning of cosec² cosec² to cot² sec² to tan²
191:53 cosec² to cot² sec² to tan² You can change it directly. So why sin
191:55 You can change it directly. So why sin And change it to cos? can you do it sin
191:58 And change it to cos? can you do it sin Why do you have to do cos butt? Ok? So I
192:01 Why do you have to do cos butt? Ok? So I I used my brain in this way that why not the boss
192:03 I used my brain in this way that why not the boss Hole square should be opened. So left hand
192:06 Hole square should be opened. So left hand Pay attention to the side. So here you go, a + b²
192:09 Pay attention to the side. So here you go, a + b² So a² means sin² is the square of the second one
192:13 So a² means sin² is the square of the second one How can someone who doesn't understand identity
192:15 How can someone who doesn't understand identity Do you want to apply it? Look at the square of the first one.
192:17 Do you want to apply it? Look at the square of the first one. do it. Square the second one. Then
192:19 do it. Square the second one. Then Write two and then multiply both.
192:21 Write two and then multiply both. Two. So keep looking at sin theta * cosec theta.
192:26 Two. So keep looking at sin theta * cosec theta. plus square the first one so cos²
192:30 plus square the first one so cos² theta square the second one so sec²
192:34 theta square the second one so sec² theta plus 2 * by multiplying both of them
192:37 theta plus 2 * by multiplying both of them 2 cos theta * sec theta Now look at this also
192:41 2 cos theta * sec theta Now look at this also Keep in mind that sin theta * cosec
192:44 Keep in mind that sin theta * cosec Theta is one. Why so? cosec theta
192:48 Theta is one. Why so? cosec theta You will write it as 1 /sin theta. cosec theta
192:50 You will write it as 1 /sin theta. cosec theta Write 1 /sin theta so sin theta to sin theta
192:53 Write 1 /sin theta so sin theta to sin theta It got cut.
192:55 It got cut. Ok? But I am doing it for you guys
192:56 Ok? But I am doing it for you guys Look here for Ok? Now pay attention. sin²
193:02 Look here for Ok? Now pay attention. sin² + cos²
193:04 + cos² What happens? Forest. So why not go with it
193:08 What happens? Forest. So why not go with it I wrote. sin² theta + cos² theta. cosec²
193:14 I wrote. sin² theta + cos² theta. cosec² Wrote to. Let me write cosec² separately. Then
193:18 Wrote to. Let me write cosec² separately. Then I will tell you what I want to say.
193:21 I will tell you what I want to say. Ok? I'll write sec² separately. sec²
193:25 Ok? I'll write sec² separately. sec² differentiating over here went to 2sin cosec so 2sinθ
193:30 differentiating over here went to 2sin cosec so 2sinθ cosec theta is written as 1 / sin theta + 2 cos
193:36 cosec theta is written as 1 / sin theta + 2 cos theta sec theta written as 1 / cos theta cos
193:40 theta sec theta written as 1 / cos theta cos theta to cos theta sin theta to sin theta
193:43 theta to cos theta sin theta to sin theta keep listening
193:45 keep listening sin² + cos² is 1 written as 1 + cosec²
193:50 sin² + cos² is 1 written as 1 + cosec² Why 1 + cot² because I said cosec²
193:55 Why 1 + cot² because I said cosec² You can directly convert it to cot²
193:57 You can directly convert it to cot² Are. Similarly, you wrote sec² as 1 + tan²
194:03 Are. Similarly, you wrote sec² as 1 + tan² There is identity. Pay to save here. Pay Here To
194:06 There is identity. Pay to save here. Pay Here To Saved. The answer has come. 1 + 1 2 + 1 3 + 4 7
194:11 Saved. The answer has come. 1 + 1 2 + 1 3 + 4 7 So 7 + 7 + cot² theta + tan² theta. Without
194:18 So 7 + 7 + cot² theta + tan² theta. Without You have proved that even if you change it to sin cos
194:22 You have proved that even if you change it to sin cos Identity. How did you think about it? if you understand
194:26 Identity. How did you think about it? if you understand two things if cosec² theta comes here
194:29 two things if cosec² theta comes here cosec² theta can be written as 1 + cot² theta
194:33 cosec² theta can be written as 1 + cot² theta yes. You will get the cot directly. sec²
194:36 yes. You will get the cot directly. sec² You can convert theta to tan² theta
194:38 You can convert theta to tan² theta yes. tan² theta will be found. 2ab 2sin theta
194:43 yes. tan² theta will be found. 2ab 2sin theta cosec theta. Whenever you get sin theta cosec
194:46 cosec theta. Whenever you get sin theta cosec Theta Simultaneous Multiplication in the Brain
194:48 Theta Simultaneous Multiplication in the Brain I should walk in. cosec theta to 1 /sin sin
194:51 I should walk in. cosec theta to 1 /sin sin From sin is gone, only two will remain. in this way
194:53 From sin is gone, only two will remain. in this way You have to use your brain. And you know this NCERT
194:56 You have to use your brain. And you know this NCERT It is a question of. CBSE this year 2025
194:59 It is a question of. CBSE this year 2025 Look what question was asked? You direct
195:02 Look what question was asked? You direct Will you answer it? CBSE
195:06 Will you answer it? CBSE Question of 2025 which paper is a bit tough
195:08 Question of 2025 which paper is a bit tough It was said for many years.
195:11 It was said for many years. So what question was asked? Exactly the same
195:14 So what question was asked? Exactly the same Question. Exactly the same question. To you
195:17 Question. Exactly the same question. To you Said find the value of x. of x from you
195:20 Said find the value of x. of x from you Asked to find out the value. Ok? Your
195:24 Asked to find out the value. Ok? Your There is no value of x. But the ones here x
195:26 There is no value of x. But the ones here x The value of is. You know that value
195:27 The value of is. You know that value What is? x = 7 will come. How? He you
195:31 What is? x = 7 will come. How? He you Do you know. Look sin + cosec cos + sec here
195:36 Do you know. Look sin + cosec cos + sec here See. sin + cosec cos + sec
195:40 See. sin + cosec cos + sec 7 + tan² + cot²
195:44 7 + tan² + cot² x + tan² + cot²
195:47 x + tan² + cot² understood? It is not to direct but to memorize
195:50 understood? It is not to direct but to memorize Had taken. Seven answers came in it. In this
195:52 Had taken. Seven answers came in it. In this The intake will also come. Have to do it. Ok? Let's move forward
195:56 The intake will also come. Have to do it. Ok? Let's move forward Let's grow. Very nice question. see
195:59 Let's grow. Very nice question. see stay. Be patient. Just be patient. I
196:01 stay. Be patient. Just be patient. I I will handle everything. Okay, right? Let's be very
196:04 I will handle everything. Okay, right? Let's be very Lovely question. Now what will your mind do here?
196:06 Lovely question. Now what will your mind do here? Buddy? A sec has to be changed to cosec. Correct
196:09 Buddy? A sec has to be changed to cosec. Correct Is? Think of things in terms of sin cos. sin
196:12 Is? Think of things in terms of sin cos. sin Think things through cos. Ok? So
196:14 Think things through cos. Ok? So Dude here sin + sec cos + cosec okay
196:17 Dude here sin + sec cos + cosec okay Is? So now this is a bit strange to me.
196:20 Is? So now this is a bit strange to me. It seems. Ok? Either you directly
196:24 It seems. Ok? Either you directly Hole Square Open Direct Hole
196:25 Hole Square Open Direct Hole There is no use in saying square. Because if
196:27 There is no use in saying square. Because if Your 2sin
196:30 Your 2sin If sec comes then it means 2ab comes then sin * sec
196:32 If sec comes then it means 2ab comes then sin * sec It will not cut.
196:35 It will not cut. You can do it but don't do it. What is the easy way?
196:39 You can do it but don't do it. What is the easy way? If you don't understand anything then sin cos
196:41 If you don't understand anything then sin cos I make the change myself. Ok? So here
196:43 I make the change myself. Ok? So here Listen left hand side sin is written as sin
196:47 Listen left hand side sin is written as sin sec is written as 1 / cos ok? Listening Meditation
196:51 sec is written as 1 / cos ok? Listening Meditation From. Ok? Here cos + cosec is written
196:54 From. Ok? Here cos + cosec is written Written 1 / sin whole square. Now please open it
196:57 Written 1 / sin whole square. Now please open it Hole Square. So the square of the first one
197:00 Hole Square. So the square of the first one Square of the second one + 2 * Buy In
197:04 Square of the second one + 2 * Buy In If you multiply both then 2 * sin * 1
197:07 If you multiply both then 2 * sin * 1 / cos² plus the square of the first one cos²
197:11 / cos² plus the square of the first one cos² The square of the second one is 1² sin of 1
197:13 The square of the second one is 1² sin of 1 square sin² of square sin
197:16 square sin² of square sin stay tuned plus 2 * cos * 1 /sin hey
197:22 stay tuned plus 2 * cos * 1 /sin hey Its square is its square 2 * both of these
197:25 Its square is its square 2 * both of these What do we do now? Now brainstorm that boss sin²
197:28 What do we do now? Now brainstorm that boss sin² + cos² is visible here so why not
197:31 + cos² is visible here so why not We could have done it together. Then sin² + cos² is 1
197:34 We could have done it together. Then sin² + cos² is 1 Went. Now you look at 1 / cos² and 1 / sin²
197:39 Went. Now you look at 1 / cos² and 1 / sin² Why don't you do it together? plus 2 * sin 2 1
197:43 Why don't you do it together? plus 2 * sin 2 1 / cos then 2sin / cos + 2 cos / sin I
197:49 / cos then 2sin / cos + 2 cos / sin I What did you do? What did I do brother? sin² +
197:51 What did you do? What did I do brother? sin² + cos² 1 / cos² 1 / sin² looks like
197:55 cos² 1 / cos² 1 / sin² looks like And this and this look similar. So
197:59 And this and this look similar. So Why not take it along? Now what
198:01 Why not take it along? Now what should I? What do you feel like doing now? From LCM
198:03 should I? What do you feel like doing now? From LCM Let's take the LCM. Ok? So this
198:06 Let's take the LCM. Ok? So this OnePlus Pay attention. pay attention. Very
198:10 OnePlus Pay attention. pay attention. Very Watch comfortably. Ok? Ok? So boss, this
198:13 Watch comfortably. Ok? Ok? So boss, this Your if you take the LCM of cos² sin²
198:16 Your if you take the LCM of cos² sin² cos² sin² cos² cos² cos² cos² left sin²
198:21 cos² sin² cos² cos² cos² cos² left sin² So sin² * 1 sin² sin² sin² sin² sin² left
198:26 So sin² * 1 sin² sin² sin² sin² sin² left cos² so cos² * 1 cos² plus focusing cos
198:30 cos² so cos² * 1 cos² plus focusing cos and LCM of sin cosin cos cos cos cos
198:34 and LCM of sin cosin cos cos cos cos So sin left over is 2sin * sin
198:37 So sin left over is 2sin * sin 2sin² sins sin sin left cos cos cos
198:41 2sin² sins sin sin left cos cos cos * 2 cos 2 cos²
198:44 * 2 cos 2 cos² The answer is coming. The answer is coming. Wait Wait
198:46 The answer is coming. The answer is coming. Wait Wait Wait Patience sin² + cos² Udi Baba Ye To Van
198:50 Wait Patience sin² + cos² Udi Baba Ye To Van So 1 / sin² is cos² plus right?
198:54 So 1 / sin² is cos² plus right? Look here, if I direct you, if you too
198:57 Look here, if I direct you, if you too Take out the common two, take out the common so this is your 2
199:01 Take out the common two, take out the common so this is your 2 sin² + cos²
199:03 sin² + cos² sin² + cos² will become one. So not this
199:06 sin² + cos² will become one. So not this I write. So 2/cosin comes out.
199:10 I write. So 2/cosin comes out. Ok? Now I need sec cosec. sec
199:14 Ok? Now I need sec cosec. sec Need cosec. sec cosec is required. sec cosec
199:17 Need cosec. sec cosec is required. sec cosec How am I changing? Look 1 + 1 /
199:20 How am I changing? Look 1 + 1 / sin². cosec² theta. pay attention. 1
199:24 sin². cosec² theta. pay attention. 1 / sin² is cosec² theta is 1 / cos²
199:29 / sin² is cosec² theta is 1 / cos² is sec² theta plus 1 / brother over here into 1
199:34 is sec² theta plus 1 / brother over here into 1 * 1 then 1 / cos 2 sec theta 1 / sin cosec
199:40 * 1 then 1 / cos 2 sec theta 1 / sin cosec Theta Now you look carefully whether this whole
199:44 Theta Now you look carefully whether this whole I need to understand this a little bit.
199:48 I need to understand this a little bit. in the space of the whole thing 1 + cosec theta * sec
199:54 in the space of the whole thing 1 + cosec theta * sec Cannot write the whole square of sec theta
199:56 Cannot write the whole square of sec theta Which you should have brought as well. hey cosec * sec
199:59 Which you should have brought as well. hey cosec * sec Say sec * cosec, it's the same thing. 3 *
200:02 Say sec * cosec, it's the same thing. 3 * 2 2 * 3 is the same thing. How is it written like this?
200:05 2 2 * 3 is the same thing. How is it written like this? Please write it brother. a + b a + b whole square then
200:10 Please write it brother. a + b a + b whole square then Its square is first 1² 1 then its
200:13 Its square is first 1² 1 then its square so its square cosec² sec² this
200:16 square so its square cosec² sec² this See. Then 2 * by this * look at this 2se
200:21 See. Then 2 * by this * look at this 2se cosec
200:22 cosec That is to say, if you solve this,
200:26 That is to say, if you solve this, This same expression will appear.
200:31 This same expression will appear. Change it to basic sin cos at last
200:33 Change it to basic sin cos at last cosec changed to sec. Next Question
200:36 cosec changed to sec. Next Question Very simple brother, he is speaking straight forward.
200:40 Very simple brother, he is speaking straight forward. Change it to sin cos. So let's come to all things
200:42 Change it to sin cos. So let's come to all things Let's change it to sin cos. Simple. So
200:44 Let's change it to sin cos. Simple. So This is already given in sin cos. This
200:46 This is already given in sin cos. This We do. Don't be afraid. a little bit bigger too
200:48 We do. Don't be afraid. a little bit bigger too If you go then there will be no tension. Brother, I wrote here
200:51 If you go then there will be no tension. Brother, I wrote here 1 + cot is written as cos / sin tan
200:55 1 + cot is written as cos / sin tan Keep watching sin / cos. Divided by Sorry
200:58 Keep watching sin / cos. Divided by Sorry written here sin - cos whole divided by
201:02 written here sin - cos whole divided by sec written as 1 / cos cosec written as 1 /
201:06 sec written as 1 / cos cosec written as 1 / sin
201:07 sin What should I do now? then change it to sin cos
201:09 What should I do now? then change it to sin cos Gave. Basic Simplification What Do You Want to Do?
201:12 Gave. Basic Simplification What Do You Want to Do? Will you do it down? LCM over LCM also taking LCM
201:14 Will you do it down? LCM over LCM also taking LCM Are. LCM to LCM
201:17 Are. LCM to LCM 1 LCM of sin and cos sin cos Attention
201:20 1 LCM of sin and cos sin cos Attention Pay attention. Ok? So what about in the forest?
201:23 Pay attention. Ok? So what about in the forest? Should I multiply? sin cos came. sin cos then
201:25 Should I multiply? sin cos came. sin cos then sin cos * 1 sin cos sin sin sin sin left
201:30 sin cos * 1 sin cos sin sin sin sin left cos so cos * cos cos² cos cos cos cos
201:35 cos so cos * cos cos² cos cos cos cos The remaining sin is sin * sin sin²
201:39 The remaining sin is sin * sin sin² This is how sin-cos is going on here.
201:43 This is how sin-cos is going on here. Divided by cos sin below LCM cos
201:48 Divided by cos sin below LCM cos sin divided by cos cos
201:51 sin divided by cos cos cos cos left sin then sin * 1 sin
201:55 cos cos left sin then sin * 1 sin sin sin sin sin left cos cos * 1 cos
202:05 Patience Patience Patience Patience Okay now You know the one at the bottom goes to the top
202:10 You know the one at the bottom goes to the top And this happens between the two of us.
202:12 And this happens between the two of us. No son, the one at the bottom goes to the top
202:16 No son, the one at the bottom goes to the top Multiply and the rest of them together so cos
202:19 Multiply and the rest of them together so cos If you multiply sin by going up, this is what you get.
202:22 If you multiply sin by going up, this is what you get. sin² + cos² + sin²
202:28 sin² + cos² + sin² * sin - cos * cos sin cos sin
202:35 * sin - cos * cos sin cos sin Divided by what is left below? sin cos brother
202:38 Divided by what is left below? sin cos brother The denominator of the top one is sin cos of the bottom one.
202:41 The denominator of the top one is sin cos of the bottom one. Numerator of sin - cos
202:43 Numerator of sin - cos So sin cos over here sin - cos
202:52 Now if you think about it, there's something here that You don't need 100%. We need sin cos.
202:56 You don't need 100%. We need sin cos. sin cos has to be changed to sin cos
202:59 sin cos has to be changed to sin cos Here's something you're not 100% sure about.
203:01 Here's something you're not 100% sure about. Needed Guess what that is?
203:04 Needed Guess what that is? Cube what everyone a
203:07 Cube what everyone a - Do you know the identity of b? who does not know
203:10 - Do you know the identity of b? who does not know Write it down. a - b a²
203:14 Write it down. a - b a² + b²
203:16 + b² a² + ab + a² + b² + ab is the identity a
203:24 a² + ab + a² + b² + ab is the identity a - of b. So here I put sin cos
203:28 - of b. So here I put sin cos Well, now you must be thinking that I have planted this in one
203:30 Well, now you must be thinking that I have planted this in one Why didn't you write? There is a reason behind it.
203:32 Why didn't you write? There is a reason behind it. Listen carefully. Ok? How do we understand
203:34 Listen carefully. Ok? How do we understand Will I come? Stop, stop. Be patient.
203:37 Will I come? Stop, stop. Be patient. Ok? Look here. So this sin - cos this cos
203:41 Ok? Look here. So this sin - cos this cos sin
203:43 sin Pay attention to your sin * cos below. sin-
203:48 Pay attention to your sin * cos below. sin- cos a - b instead of a - b
203:53 cos a - b instead of a - b square of the other one + ab
203:58 square of the other one + ab Look at the benefit, what has happened is that
204:00 Look at the benefit, what has happened is that sin - cos to sin - cos sin² + cos² + sin
204:05 sin - cos to sin - cos sin² + cos² + sin cos sin² + cos² + sin cos yr 1 + 2 + 3
204:10 cos sin² + cos² + sin cos yr 1 + 2 + 3 It is written. 3 + 2 + 1 is written. 2 + 1 + 3
204:12 It is written. 3 + 2 + 1 is written. 2 + 1 + 3 It is written. It's all the same thing. So sin cos sin
204:15 It is written. It's all the same thing. So sin cos sin cos cos² cos² sin² sin² in all three plus
204:18 cos cos² cos² sin² sin² in all three plus So this whole thing will be cut off by this.
204:22 So this whole thing will be cut off by this. Ok?
204:24 Ok? One sin minus one sin will leave sin². a cos
204:27 One sin minus one sin will leave sin². a cos One cos then cos² will remain. if you think
204:31 One cos then cos² will remain. if you think Get it. So what's left? cos²
204:34 Get it. So what's left? cos² sin² which is what you needed.
204:37 sin² which is what you needed. cos² sin² which is what you needed.
204:41 cos² sin² which is what you needed. This type of questions are there in trigonometry.
204:43 This type of questions are there in trigonometry. Are.
204:48 I hope you guys are enjoying it. Now! There are a lot of questions to ask. right now
204:50 There are a lot of questions to ask. right now There are so many previous year questions that
204:52 There are so many previous year questions that You can't even imagine. Let's move ahead. Let us go
204:56 You can't even imagine. Let's move ahead. Let us go Now let's move on to the next set of questions.
204:57 Now let's move on to the next set of questions. Look friend, it's going to be fun. Now no LCM
205:00 Look friend, it's going to be fun. Now no LCM It is a dangerous game. I will show you.
205:02 It is a dangerous game. I will show you. What do you want to do brother? The dude is speaking for himself
205:04 What do you want to do brother? The dude is speaking for himself Shout and change it to sin cos
205:06 Shout and change it to sin cos So do it. Ok. Let us go. So cos and sin then
205:10 So do it. Ok. Let us go. So cos and sin then It already is. tan and cot into sin cos
205:12 It already is. tan and cot into sin cos I have to change it. Let's do it. Then cos
205:14 I have to change it. Let's do it. Then cos what I wrote? Left hand side. cos to
205:17 what I wrote? Left hand side. cos to I wrote cos comfortably. Now listen to cos
205:21 I wrote cos comfortably. Now listen to cos If I plant a forest below, why would there be a problem?
205:23 If I plant a forest below, why would there be a problem? I am doing this so that there is no confusion brother.
205:25 I am doing this so that there is no confusion brother. I am feeling confused. 1 - sin instead of tan
205:29 I am feeling confused. 1 - sin instead of tan / cos brother. What is going on? that fear
205:31 / cos brother. What is going on? that fear I am not able to understand. Hey friend this
205:33 I am not able to understand. Hey friend this The thought of buying LCM as soon as I saw it
205:35 The thought of buying LCM as soon as I saw it Needed Ok? Look here, just look at the plus sin
205:39 Needed Ok? Look here, just look at the plus sin Substitute 1 / 1 - cot instead of cos/sin
205:44 Substitute 1 / 1 - cot instead of cos/sin So everything has changed in sin cos. Just now
205:46 So everything has changed in sin cos. Just now Have to simplify. Yes, let's. So
205:50 Have to simplify. Yes, let's. So LCM will have to be taken here. Ok? So
205:52 LCM will have to be taken here. Ok? So Up cos / 1d by cos went here brother. here
205:58 Up cos / 1d by cos went here brother. here If one is below then the LCM of one and cos is cos
206:00 If one is below then the LCM of one and cos is cos Will come. Then what should I multiply in one?
206:02 Will come. Then what should I multiply in one? If cos comes then cos then cos will go up. So
206:05 If cos comes then cos then cos will go up. So I am directing it. try to understand
206:06 I am directing it. try to understand What if cos went up then this cos - sin /
206:10 What if cos went up then this cos - sin / cos + sin / 1 this is your sin gone up so sin
206:15 cos + sin / 1 this is your sin gone up so sin I understand cos/sin now.
206:19 I understand cos/sin now. What will happen if there is no confusion then below
206:21 What will happen if there is no confusion then below The one at the top is the lowest among themselves.
206:24 The one at the top is the lowest among themselves. Above these are okay with each other so cos go cos
206:27 Above these are okay with each other so cos go cos I went into cos and then it came to cos²
206:32 I went into cos and then it came to cos² Okay cos - sin going into the forest then this cos -
206:35 Okay cos - sin going into the forest then this cos - sin plus is okay. sin go and sin so this
206:39 sin plus is okay. sin go and sin so this Here comes sin² and here comes your sin -
206:42 Here comes sin² and here comes your sin - cos now
206:45 cos now There is a slight twist here. here
206:48 There is a slight twist here. here Tell me what you would like to do? LCM
206:50 Tell me what you would like to do? LCM To take. But tell me if 1/2 + 1/
206:55 To take. But tell me if 1/2 + 1/ If it is written 3 then friend take this little LCM
206:58 If it is written 3 then friend take this little LCM Will have to. Then the numerator will have to be changed.
207:00 Will have to. Then the numerator will have to be changed. But if it is written 1/2 + 3/2, it means if
207:04 But if it is written 1/2 + 3/2, it means if If the denominator is the same, the numerator changes.
207:07 If the denominator is the same, the numerator changes. It's not going to happen. If the denominator is same then
207:09 It's not going to happen. If the denominator is same then The numerator is not going to change. My
207:11 The numerator is not going to change. My What this means is that there is no denominator here.
207:15 What this means is that there is no denominator here. There are almost beans. There is a slight difference.
207:18 There are almost beans. There is a slight difference. Now look at this + cos here - cos this
207:22 Now look at this + cos here - cos this -sin here + sin means just the difference of sin
207:26 -sin here + sin means just the difference of sin So here I know you do listening.
207:28 So here I know you do listening. I am directing it. cos² written above
207:31 I am directing it. cos² written above Listen to cos - sin written here. wrote this
207:33 Listen to cos - sin written here. wrote this I wrote plus as sin², from here I wrote minus
207:37 I wrote plus as sin², from here I wrote minus Sign common taken out. And as soon as you use the minus
207:40 Sign common taken out. And as soon as you use the minus If you remove the sign common then it will become yours
207:42 If you remove the sign common then it will become yours Minus sign. This will become + cos why so?
207:47 Minus sign. This will become + cos why so? Hear Why so? Hey boss, if this minus
207:50 Hear Why so? Hey boss, if this minus If it goes inside then plus sign. Minus went in
207:52 If it goes inside then plus sign. Minus went in So cos so if you take out the minus
207:55 So cos so if you take out the minus Wear no matter what. Why? because this is the same
207:58 Wear no matter what. Why? because this is the same It will be back.
208:00 It will be back. Do you understand what I am saying? and this
208:02 Do you understand what I am saying? and this You can call this thing + cos - sin + cos
208:06 You can call this thing + cos - sin + cos You can write - sin cos - sin. what's the problem
208:08 You can write - sin cos - sin. what's the problem Is? What's the problem? It's the same thing brother. After C
208:11 Is? What's the problem? It's the same thing brother. After C Write in, write S first or C first in S
208:14 Write in, write S first or C first in S That's it. Well, this minus sign is minus
208:17 That's it. Well, this minus sign is minus You can send the sign up or this minus
208:19 You can send the sign up or this minus You can send the sign here. I want to say this
208:22 You can send the sign here. I want to say this I have been listening carefully. This plus sign
208:26 I have been listening carefully. This plus sign I changed it. Opposited it.
208:28 I changed it. Opposited it. Made a minus. sin² here and this
208:31 Made a minus. sin² here and this I wrote cos - sin it. what are you doing
208:35 I wrote cos - sin it. what are you doing Gave? once once once once once once
208:37 Gave? once once once once once once and well? Look here. This sin - cos
208:40 and well? Look here. This sin - cos I wrote cos - sin which is written here
208:43 I wrote cos - sin which is written here And this plus was turned into minus. Finish
208:45 And this plus was turned into minus. Finish Went. I can do this. why could
208:47 Went. I can do this. why could Am? Oh, I can do it. Hey, why can I do it?
208:48 Am? Oh, I can do it. Hey, why can I do it? Oh, I can do it. Hey why? Why? Oho
208:50 Oh, I can do it. Hey why? Why? Oho I can do it. I said it. Hey why? Come on, tell me
208:52 I can do it. I said it. Hey why? Come on, tell me I have been. Look, this minus can go down here.
208:56 I have been. Look, this minus can go down here. Is. So this is cos + sin - cos + sin oh
209:00 Is. So this is cos + sin - cos + sin oh This is what was written. I can do this. Bus
209:03 This is what was written. I can do this. Bus Now what is the benefit of this? cos - sin cos - sin
209:06 Now what is the benefit of this? cos - sin cos - sin So this cos - sin bottom up numerator edge
209:09 So this cos - sin bottom up numerator edge It is not easy to take more LCM
209:12 It is not easy to take more LCM Is. Now friend, what is it like here?
209:15 Is. Now friend, what is it like here? Who is not here? what is it here
209:16 Who is not here? what is it here Who is not here? Square so a² -
209:20 Who is not here? Square so a² - b² a - b a + b and written cos - sin below
209:25 b² a - b a + b and written cos - sin below It has happened. So cos - sin went to cos - sin.
209:28 It has happened. So cos - sin went to cos - sin. cos + sin is what you need. exam
209:32 cos + sin is what you need. exam Beware, do not write c and s. cos and sin
209:36 Beware, do not write c and s. cos and sin a will have to be written in full. Ok? This
209:39 a will have to be written in full. Ok? This An excellent question of this type from NCERT
209:42 An excellent question of this type from NCERT But CBSE asked so many times
209:45 But CBSE asked so many times So many times that you can't imagine. limit reached
209:47 So many times that you can't imagine. limit reached Yes brother. Ok? Hashtag QD Question. Today
209:50 Yes brother. Ok? Hashtag QD Question. Today One of the best questions of the class
209:52 One of the best questions of the class A hashtag link from #shatag
209:56 A hashtag link from #shatag QD. Hey, move away, move away quickly. Hatg Kadi
209:59 QD. Hey, move away, move away quickly. Hatg Kadi Question. Ok? Now let me ask this question
210:02 Question. Ok? Now let me ask this question There are ways. But I will tell you the easiest way
210:04 There are ways. But I will tell you the easiest way I am giving you whatever comes to your mind.
210:07 I am giving you whatever comes to your mind. Dude, this is tan coat. Have to bring it to tan coat.
210:10 Dude, this is tan coat. Have to bring it to tan coat. Then in this you have to first understand the meaning. This means this is
210:12 Then in this you have to first understand the meaning. This means this is Here, first of all, after solving this,
210:17 Here, first of all, after solving this, Bring it. Then solve this and bring this.
210:20 Bring it. Then solve this and bring this. Solve it once again and take this
210:23 Solve it once again and take this Come. Solve this and bring this. Ok?
210:27 Come. Solve this and bring this. Ok? Do one thing. Do one thing. this question
210:30 Do one thing. Do one thing. this question You guys do it at home using the other method.
210:33 You guys do it at home using the other method. Let me tell you through one method. Second method
210:35 Let me tell you through one method. Second method The one that changes to sin cos. What? hey when
210:38 The one that changes to sin cos. What? hey when If you don't understand anything, there's nothing much to worry about.
210:40 If you don't understand anything, there's nothing much to worry about. Change it to sin cos. change in sin cos
210:42 Change it to sin cos. change in sin cos You can't do it. I will keep you in the tan coat itself
210:45 You can't do it. I will keep you in the tan coat itself I will change it and let you know. Ok? these tan cot
210:48 I will change it and let you know. Ok? these tan cot It is given in. Have to stay in tan cot. So
210:50 It is given in. Have to stay in tan cot. So Why don't I let him stay in the tan cot?
210:52 Why don't I let him stay in the tan cot? Why don't I let him stay in the tan cot?
210:53 Why don't I let him stay in the tan cot? Well, it can be done in sin cos also. But I tan
210:55 Well, it can be done in sin cos also. But I tan I'll let you stay in the cot. Ok? Now let's go
210:56 I'll let you stay in the cot. Ok? Now let's go We do. Now friend, do this in tan coat
210:58 We do. Now friend, do this in tan coat How to remember a little bit. Ok?
211:00 How to remember a little bit. Ok? Look, this is tan here. This is tan. This cot
211:04 Look, this is tan here. This is tan. This cot Is. This is a cot. What should I do? I this
211:07 Is. This is a cot. What should I do? I this I will change this cot to tan
211:09 I will change this cot to tan As such. Why?
211:11 As such. Why? Because it will make sense. Just look. Just look.
211:15 Because it will make sense. Just look. Just look. Here it is written tan, t means tan. t means
211:19 Here it is written tan, t means tan. t means Plant two forests under the tan.
211:22 Plant two forests under the tan. 1 - cot is written as 1 / tan plus cot is written as 1
211:27 1 - cot is written as 1 / tan plus cot is written as 1 / tan Write 1 / tan is it okay or a little
211:30 / tan Write 1 / tan is it okay or a little Just write cot for now, cot / 1d / 1 -
211:34 Just write cot for now, cot / 1d / 1 - tan as it is
211:37 tan as it is ok you will understand what i am doing
211:39 ok you will understand what i am doing Okay, look here, okay, if you take LCM
211:42 Okay, look here, okay, if you take LCM Look, this tan / 1 / tan above is tan - 1 /
211:47 Look, this tan / 1 / tan above is tan - 1 / tan okay tan - 1 / tan plus over here
211:52 tan okay tan - 1 / tan plus over here cot / 1 or write it directly like this cot /
211:55 cot / 1 or write it directly like this cot / 1 - tan
211:58 1 - tan Now look what I'm doing to the one above.
212:00 Now look what I'm doing to the one above. I did not make any changes above, that is right
212:02 I did not make any changes above, that is right It's okay if you don't change the one.
212:05 It's okay if you don't change the one. The one below is the top, these two are now together
212:07 The one below is the top, these two are now together Look what benefit it brought, the benefit was that
212:11 Look what benefit it brought, the benefit was that tan * tan tan tan tan tan²
212:15 tan * tan tan tan tan tan² And note that tan - 1 * 1 is tan - 1
212:19 And note that tan - 1 * 1 is tan - 1 this + cot cot this + cote by 1 - tan now
212:25 this + cot cot this + cote by 1 - tan now Why did I do this? tell me once again
212:27 Why did I do this? tell me once again I have been. Look what I did here? I
212:30 I have been. Look what I did here? I If we change this cot to 1 / tan then
212:33 If we change this cot to 1 / tan then This is tan - 1 / tan. Tan went up.
212:36 This is tan - 1 / tan. Tan went up. tan - 1 The advantage is that tan - 1 1 - tan
212:41 tan - 1 The advantage is that tan - 1 1 - tan tan - 1 1 - tan which is the denominator
212:44 tan - 1 1 - tan which is the denominator Almost almost beans. It's not a complete bean. So
212:47 Almost almost beans. It's not a complete bean. So What did I do for that? tells you
212:48 What did I do for that? tells you I just did what I could do
212:51 I just did what I could do How is this tan² written, this tan - 1 written, this
212:56 How is this tan² written, this tan - 1 written, this Change plus to minus and 1 - tan to tan
213:01 Change plus to minus and 1 - tan to tan - 1 is +1 to -1 - tan to + tan and
213:07 - 1 is +1 to -1 - tan to + tan and Here instead of plus, I will do minus like this
213:09 Here instead of plus, I will do minus like this I can. What will be the benefit? tan - 1 tan -
213:12 I can. What will be the benefit? tan - 1 tan - 1 denominator sem. So numerator you age it
213:15 1 denominator sem. So numerator you age it You can write this. once again again again
213:17 You can write this. once again again again You just look at it and understand that from here
213:20 You just look at it and understand that from here I took out the minus and put it here.
213:23 I took out the minus and put it here. this -1 this + tan because you see for yourself this
213:26 this -1 this + tan because you see for yourself this If minus goes in then - tan minus goes in then
213:29 If minus goes in then - tan minus goes in then +1 will come the same. Now look at the denominator
213:33 +1 will come the same. Now look at the denominator tan - 1 is written above as tan² - cot because
213:38 tan - 1 is written above as tan² - cot because cot odd one out so it was written as 1 / tan.
213:41 cot odd one out so it was written as 1 / tan. What's the problem? cot is written as 1 / tan
213:44 What's the problem? cot is written as 1 / tan Now if I have to take the same LCM then I get tensed.
213:46 Now if I have to take the same LCM then I get tensed. So tan² * tan tan
213:49 So tan² * tan tan - 1 / tan / tan - 1 / tan or else this
213:54 - 1 / tan / tan - 1 / tan or else this I'll write it again so there's no confusion.
213:58 I'll write it again so there's no confusion. Look to the side, look here, okay, so here.
214:02 Look to the side, look here, okay, so here. See one is one and the LCM of tan is tan
214:06 See one is one and the LCM of tan is tan Okay, what should I multiply in one?
214:08 Okay, what should I multiply in one? If tan comes tan * tan² tan
214:11 If tan comes tan * tan² tan here over here tan over here tan so up -1
214:14 here over here tan over here tan so up -1 As it is divided by now the numerator above
214:16 As it is divided by now the numerator above The denominator is tan - 1 / tan
214:21 The denominator is tan - 1 / tan Write it down, okay, upon one, write it down, sorry upon one
214:24 Write it down, okay, upon one, write it down, sorry upon one One means nothing, now that there is no confusion
214:28 One means nothing, now that there is no confusion This is at the top, this is here
214:31 This is at the top, this is here - 1 tan * tan - 1
214:36 - 1 tan * tan - 1 Now I don't want a cube here, so I want a cube.
214:39 Now I don't want a cube here, so I want a cube. If I don't want it, should I write one 1 as 1?
214:43 If I don't want it, should I write one 1 as 1? Sorry, should I replace a - b with a - b? a - b what
214:47 Sorry, should I replace a - b with a - b? a - b what It happens? a - b a² + b² + ab
214:54 It happens? a - b a² + b² + ab Ok? So if I put a - b i.e. tan -
214:58 Ok? So if I put a - b i.e. tan - 1 tan² 1² 1 + tan * 1 Got it? Its
215:03 1 tan² 1² 1 + tan * 1 Got it? Its Square, then its square, then both
215:05 Square, then its square, then both Multiply this. divided by tan *
215:08 Multiply this. divided by tan * tan - 1 Look, tan - 1 went to tan - 1.
215:12 tan - 1 Look, tan - 1 went to tan - 1. What happened in the final? tan² + 1 + tan / tan
215:16 What happened in the final? tan² + 1 + tan / tan See what comes here? tan² + 1 + tan / tan
215:22 See what comes here? tan² + 1 + tan / tan Now what did I do? tan under tan² different,
215:27 Now what did I do? tan under tan² different, Tan is different under the forest, tan is different under the tan.
215:30 Tan is different under the forest, tan is different under the tan. The answer has come. If one tan goes beyond tan then it is yours
215:34 The answer has come. If one tan goes beyond tan then it is yours Tan a answer has come. 1 / tan a is cot
215:37 Tan a answer has come. 1 / tan a is cot and this is your
215:40 and this is your tan / tan sorry this is tan / tan a isn't it tan
215:44 tan / tan sorry this is tan / tan a isn't it tan / tan a So here comes your forest. This is what you
215:47 / tan a So here comes your forest. This is what you Had to bring it. tan a + cot a + 1 tan a + cot a
215:51 Had to bring it. tan a + cot a + 1 tan a + cot a + 1 You can also convert it to sin cos and do this
215:55 + 1 You can also convert it to sin cos and do this Could have. There is no load. Ok? Correct
216:00 Could have. There is no load. Ok? Correct Is? See from the beginning. ok now this
216:02 Is? See from the beginning. ok now this How am I taking it? sec cosec direct if
216:04 How am I taking it? sec cosec direct if We have to understand that from here we have to go to sec cosec, so
216:06 We have to understand that from here we have to go to sec cosec, so What to do? Change it to sin cos. Ok?
216:10 What to do? Change it to sin cos. Ok? So you wrote sin / cos or you wrote
216:13 So you wrote sin / cos or you wrote cos / sin is your 1 / 1 obviously LCM
216:16 cos / sin is your 1 / 1 obviously LCM will have to take. Leave the forest aside.
216:19 will have to take. Leave the forest aside. Reason being, look here one is written separately
216:21 Reason being, look here one is written separately It has happened. Solve this and you will get the answer.
216:24 It has happened. Solve this and you will get the answer. LCM of cos and sin cos sin cos cos sin
216:27 LCM of cos and sin cos sin cos cos sin left sin sin sin² of sin sin sin sin cos
216:31 left sin sin sin² of sin sin sin sin cos The remaining cos * cos cos² + 1 is your result.
216:35 The remaining cos * cos cos² + 1 is your result. sin² + cos² 1 / cos sin + 1 here into
216:40 sin² + cos² 1 / cos sin + 1 here into 1 to 1 / cos sec a 1 / sin
216:46 1 to 1 / cos sec a 1 / sin cosec a + 1 you have to prove this also
216:49 cosec a + 1 you have to prove this also Gaya Easy
216:52 Gaya Easy Okay, not very easy, but
216:54 Okay, not very easy, but It is easy, meaning it is not too difficult.
216:56 It is easy, meaning it is not too difficult. Is. This is a very important question. want to see
216:58 Is. This is a very important question. want to see This again. Ok? Do as many questions as you can
217:01 This again. Ok? Do as many questions as you can I am doing this one shot in this lecture today
217:03 I am doing this one shot in this lecture today You have to repeat it in the video.
217:05 You have to repeat it in the video. There is no need to cram. Have to understand. see this
217:08 There is no need to cram. Have to understand. see this How is that coming to my mind? yours
217:10 How is that coming to my mind? yours How will it come to mind? not to memorize that
217:12 How will it come to mind? not to memorize that This is to be done after the step. then this then this
217:13 This is to be done after the step. then this then this Then not this. The question tells itself
217:15 Then not this. The question tells itself What is the plan. Like the question here
217:18 What is the plan. Like the question here I told you, boss, I don't have a cube.
217:20 I told you, boss, I don't have a cube. I need it friend. Remove this cube, friend. then a - b
217:23 I need it friend. Remove this cube, friend. then a - b Came to mind. Ok? here if
217:26 Came to mind. Ok? here if Look, if I write this as 1 / tan, then this
217:29 Look, if I write this as 1 / tan, then this tan - 1 so somewhere the denominator is the same
217:31 tan - 1 so somewhere the denominator is the same Can be made. So why not make it? Correct
217:35 Can be made. So why not make it? Correct Is? After that, this denominator is separated by
217:38 Is? After that, this denominator is separated by Is. How did it come to your mind? tan below tan²
217:40 Is. How did it come to your mind? tan below tan² So tan 1 / tan cot is what we need. So
217:43 So tan 1 / tan cot is what we need. So The denominator has to be separated.
217:46 The denominator has to be separated. And that's what is needed. Come on man, it's a very cute one
217:49 And that's what is needed. Come on man, it's a very cute one Question. Ok? Now what is this mind here?
217:52 Question. Ok? Now what is this mind here? Am I coming brother? Have to bring the forest. Forest Fetching
217:54 Am I coming brother? Have to bring the forest. Forest Fetching Is. Have to bring the forest. Ok? Now look at this
217:59 Is. Have to bring the forest. Ok? Now look at this Based on what questions CBSE asked this year
218:01 Based on what questions CBSE asked this year Did you ask? To focus. Ok? So brother one
218:05 Did you ask? To focus. Ok? So brother one Have to bring it. Meaning everything is getting cancelled.
218:07 Have to bring it. Meaning everything is getting cancelled. Must be. When do things get cancelled? When beans
218:08 Must be. When do things get cancelled? When beans Are there. Brother, here's something that
218:11 Are there. Brother, here's something that It is disturbing me. That is power
218:12 It is disturbing me. That is power Four. So the power four into comfortable power
218:16 Four. So the power four into comfortable power Get it converted. Not in my mind because
218:18 Get it converted. Not in my mind because Nothing else is coming to my mind, boss. sin
218:20 Nothing else is coming to my mind, boss. sin I am comfortable in cos. sin cos
218:22 I am comfortable in cos. sin cos is given. I felt like this even in the square.
218:24 is given. I felt like this even in the square. There is no problem. I'm screwed with the Power Four.
218:26 There is no problem. I'm screwed with the Power Four. I change the power four. But its
218:28 I change the power four. But its For this you need to know an identity. a²
218:31 For this you need to know an identity. a² a + b² is a + b²
218:35 a + b² is a + b² - 2ab this identity which is not a child
218:38 - 2ab this identity which is not a child I know, please take note. too much
218:42 I know, please take note. too much Identity is important. very much
218:45 Identity is important. very much Identity is important. Ok? Ok?
218:50 Identity is important. Ok? Ok? What? a² brother you know a + b². a² +
218:54 What? a² brother you know a + b². a² + What is b²? a² + b². a + b²
218:58 What is b²? a² + b². a + b² - 2ab okay? So come to power four I
219:01 - 2ab okay? So come to power four I I am not comfortable. So I called the power four
219:03 I am not comfortable. So I called the power four What did you write?
219:05 What did you write? Square of Square.
219:07 Square of Square. Square of Square.
219:10 Square of Square. Ok? I am solving sin separately.
219:12 Ok? I am solving sin separately. To explain to you the power of 4 + cos of power 4
219:15 To explain to you the power of 4 + cos of power 4 For. So sin to the power of 4 is sin²
219:18 For. So sin to the power of 4 is sin² square cos to the power of 4 and cos²
219:20 square cos to the power of 4 and cos² Square. Now what happened here? If you
219:21 Square. Now what happened here? If you Look, what is a² + b² a² + b²? a
219:28 Look, what is a² + b² a² + b²? a + b²
219:31 + b² - 2ab
219:34 - 2ab Did you understand? once again a
219:37 Did you understand? once again a once again once again brother a² + b²
219:41 once again once again brother a² + b² What happens? a² + b² a² + b² a + b² -
219:45 What happens? a² + b² a² + b² a + b² - 2ab a + b² - 2ab So this is a, this is b, this
219:51 2ab a + b² - 2ab So this is a, this is b, this a is this, b is this, a is this, b is this, then a +
219:55 a is this, b is this, a is this, b is this, then a + b² - 2ab Got it? Look what came? So sin²
220:01 b² - 2ab Got it? Look what came? So sin² + cos² 1 so 1 squared is 1 so this is your 1
220:04 + cos² 1 so 1 squared is 1 so this is your 1 - 2sin² cos² arrived. 1 - 2sin² cos² then
220:09 - 2sin² cos² arrived. 1 - 2sin² cos² then sin to the power of 4 + cos to the power of 4 is 1 -
220:13 sin to the power of 4 + cos to the power of 4 is 1 - We can write 2sin² cos². So if I
220:16 We can write 2sin² cos². So if I If I go directly to the question, then the left hand
220:19 If I go directly to the question, then the left hand What became of the side? You have given the one above
220:21 What became of the side? You have given the one above Converted 1 - 2sin² to cos². Below
220:25 Converted 1 - 2sin² to cos². Below Look, 1 - 2 sin² is in cos².
220:29 Look, 1 - 2 sin² is in cos². The answer has come. 1 - 2sin² cos² 1 - 2sin²
220:33 The answer has come. 1 - 2sin² cos² 1 - 2sin² cos² Answer Aa Gaya One. tell me once again
220:36 cos² Answer Aa Gaya One. tell me once again I have been. Ok? sin to the power of 4 + cos
220:39 I have been. Ok? sin to the power of 4 + cos You wrote sin² cos² to the power of 4, so a² + b²
220:45 You wrote sin² cos² to the power of 4, so a² + b² a² + b² a + b² - 2ab
220:51 a² + b² a + b² - 2ab Ok? So sin to the power of 4 + cos to the power of 4
220:54 Ok? So sin to the power of 4 + cos to the power of 4 here comes the. So sin to the power of 4 + cos to the power
220:57 here comes the. So sin to the power of 4 + cos to the power Wrote this instead of 4. The forest has just been cut down
221:00 Wrote this instead of 4. The forest has just been cut down Went. Now see what CBSE has done this year
221:04 Went. Now see what CBSE has done this year You asked a lovely question on this concept.
221:06 You asked a lovely question on this concept. CBSE said that bos sin theta + cos
221:09 CBSE said that bos sin theta + cos theta x is given. CBSE
221:12 theta x is given. CBSE This question came in the 2025 paper.
221:17 This question came in the 2025 paper. I know the child lecture is big.
221:19 I know the child lecture is big. But if you're still in this lecture
221:21 But if you're still in this lecture No, with sincerity and discipline
221:24 No, with sincerity and discipline You will break the CBSE board
221:26 You will break the CBSE board Trigonometry. So this is my guarantee.
221:28 Trigonometry. So this is my guarantee. Ok? I live in the forest like the rest of the people
221:30 Ok? I live in the forest like the rest of the people I don't make shots that take 2 hours.
221:33 I don't make shots that take 2 hours. I gave it and just made it. Give one shot for 2 hours
221:36 I gave it and just made it. Give one shot for 2 hours That anyone can see it. But none of that
221:38 That anyone can see it. But none of that It's not going to be beneficial. Ok? you
221:41 It's not going to be beneficial. Ok? you Questions will not be made from any book only when you
221:44 Questions will not be made from any book only when you A good one-shot watch. Ok? so you
221:48 A good one-shot watch. Ok? so you Just keep going till the end. Ok? Let us go. So
221:51 Just keep going till the end. Ok? Let us go. So sin theta + cos theta x is given. Correct
221:53 sin theta + cos theta x is given. Correct Is it boss? Good proof that sin has the power of 4+
221:56 Is it boss? Good proof that sin has the power of 4+ cos to the power of 4 is equal to this. Prove That
221:59 cos to the power of 4 is equal to this. Prove That sin to the power of 4 + cos to the power of 4 is equal to
222:01 sin to the power of 4 + cos to the power of 4 is equal to will be. Ok?
222:03 will be. Ok? Ok? What do I have to understand brother? Left
222:06 Ok? What do I have to understand brother? Left Solving the right hand side and getting the right hand side
222:08 Solving the right hand side and getting the right hand side Is. But how will this x etc. come? will see later
222:10 Is. But how will this x etc. come? will see later I will see it later. One thing to me
222:12 I will see it later. One thing to me Do you know what boss, if I am left handed
222:15 Do you know what boss, if I am left handed If I raise the side, sin to the power of 4 + cos
222:19 If I raise the side, sin to the power of 4 + cos I learned to solve Power 4. These
222:22 I learned to solve Power 4. These square of sin² is square of cos² so
222:26 square of sin² is square of cos² so What is a² + b²? a + b²
222:32 What is a² + b²? a + b² - 2 ab ab sin² + cos² 1 so square of 1
222:38 - 2 ab ab sin² + cos² 1 so square of 1 One, here we go: 1 - 2sin² cos² 1 - 2sin²
222:42 One, here we go: 1 - 2sin² cos² 1 - 2sin² cos² 1 - 2sin² cos² Okay, that's it. But
222:48 cos² 1 - 2sin² cos² Okay, that's it. But How do I bring this? So much has come but this
222:50 How do I bring this? So much has come but this How do I bring it? I am not able to understand this. These
222:53 How do I bring it? I am not able to understand this. These How will everything come? Good means replacing it with x
222:57 How will everything come? Good means replacing it with x Is. Replace it with x. Now listen carefully
222:58 Is. Replace it with x. Now listen carefully From. Something has been given to me. to me
223:00 From. Something has been given to me. to me Given sinθ + cosθ is equal to x. sinθ
223:05 Given sinθ + cosθ is equal to x. sinθ equals x + cos theta. pay attention.
223:10 equals x + cos theta. pay attention. I have sin cos. sin is cos. sin cos
223:13 I have sin cos. sin is cos. sin cos Is. I have sin + cos. sin + cos.
223:16 Is. I have sin + cos. sin + cos. I will ask you more such questions in future.
223:17 I will ask you more such questions in future. I will get it done. sin + cos is given. Finding sin cos
223:20 I will get it done. sin + cos is given. Finding sin cos Is. sin + cos is given. sin cos brother to you
223:23 Is. sin + cos is given. sin cos brother to you We will have to find the value of sin cos. Then
223:26 We will have to find the value of sin cos. Then If you go, some x will come. So if sin +
223:29 If you go, some x will come. So if sin + cos is given. We have to find sin cos. Now both
223:31 cos is given. We have to find sin cos. Now both Do side squaring. See what the benefit is
223:33 Do side squaring. See what the benefit is will be? Now you will speak your mind
223:35 will be? Now you will speak your mind How will it come? By practice. take a look first
223:37 How will it come? By practice. take a look first To me. sin + cos here whole square and
223:41 To me. sin + cos here whole square and Hole square here. See what's going on here
223:42 Hole square here. See what's going on here Is? So this is your sin² + cos² + 2sin cos =
223:47 Is? So this is your sin² + cos² + 2sin cos = x² Pay attention What's happening? So this 1+
223:50 x² Pay attention What's happening? So this 1+ 2sin cos = x² then 2sin cos = x² – 1 then
223:56 2sin cos = x² then 2sin cos = x² – 1 then The value of sin cos is x² - 1 / 2
224:02 The value of sin cos is x² - 1 / 2 Ok? And if you want a square here,
224:04 Ok? And if you want a square here, Both sides square means both sides
224:06 Both sides square means both sides Do the squaring. both sides again
224:07 Do the squaring. both sides again squared so sin² cos² this is your x² - 1/2
224:12 squared so sin² cos² this is your x² - 1/2 Whole Square of. Did you understand this thing? Understanding
224:17 Whole Square of. Did you understand this thing? Understanding What came in? Very important, very sweet
224:20 What came in? Very important, very sweet It's a thing. Ok? telling me once again
224:22 It's a thing. Ok? telling me once again Am. If sin + cos is given then you can find sin *
224:25 Am. If sin + cos is given then you can find sin * You can bring cos. How? both sides
224:28 You can bring cos. How? both sides Do the squaring. So its square is
224:31 Do the squaring. So its square is Square that will come to One. sin cos escape
224:34 Square that will come to One. sin cos escape Will go. So you get sin cos sin from sin + cos
224:36 Will go. So you get sin cos sin from sin + cos + cos will give sin cos. Ok? Correct
224:40 + cos will give sin cos. Ok? Correct Is? So boss, what happened? 2sin cos 1 went there
224:43 Is? So boss, what happened? 2sin cos 1 went there The value of x² - 1 sin cos is x² - 1 / 2 now
224:47 The value of x² - 1 sin cos is x² - 1 / 2 now sin if you square both sides again
224:49 sin if you square both sides again If you do this then the value of sin² cos² is x² - 1
224:53 If you do this then the value of sin² cos² is x² - 1 Hole Square of /2. Just put it here
224:56 Hole Square of /2. Just put it here to the thing. So instead of 1 - 2 sin² cos² we get x² - 1
225:04 to the thing. So instead of 1 - 2 sin² cos² we get x² - 1 / 2's whole square somewhere somewhere
225:07 / 2's whole square somewhere somewhere Somewhere we reached there. But here two
225:09 Somewhere we reached there. But here two Should and should below two. So I took the LCM
225:11 Should and should below two. So I took the LCM What should I do to get LCM from? Attention
225:13 What should I do to get LCM from? Attention Pay attention here, pay attention here. So this is what I
225:15 Pay attention here, pay attention here. So this is what I Wrote 1 - 2
225:18 Wrote 1 - 2 x² - 1²
225:21 x² - 1² And 2 hole square at the bottom. What's the problem?
225:24 And 2 hole square at the bottom. What's the problem? Square above is different, square below is different. So
225:26 Square above is different, square below is different. So What was the benefit? 2² means 4 so 4 here
225:30 What was the benefit? 2² means 4 so 4 here If you take the LCM, you can do 4 - 2 or even this
225:34 If you take the LCM, you can do 4 - 2 or even this yes. 2 * 1 2 * 2 so 1 - x² - 1²
225:41 yes. 2 * 1 2 * 2 so 1 - x² - 1² / 2 Take the LCM. The answer has come. So 2 - x²
225:46 / 2 Take the LCM. The answer has come. So 2 - x² - 1² / 2
225:50 - 1² / 2 Very nice question. This is called qt, isn't it?
225:53 Very nice question. This is called qt, isn't it? To the question.
225:55 To the question. That was a very good question. Very good question.
225:58 That was a very good question. Very good question. Ok? Is it clear? Two concepts here
226:02 Ok? Is it clear? Two concepts here But you learned. One that I just told you
226:04 But you learned. One that I just told you Previously taught that the power of sin is 4 +
226:07 Previously taught that the power of sin is 4 + How to solve cos to the power of 4.
226:09 How to solve cos to the power of 4. Every child can reach here. Then
226:11 Every child can reach here. Then How to convert this thing into x? Attention
226:15 How to convert this thing into x? Attention Applied. Need the value of sin cos. sin cos
226:17 Applied. Need the value of sin cos. sin cos The value of is required. sin + cos is given.
226:20 The value of is required. sin + cos is given. Squaring both sides. The work got done.
226:24 Squaring both sides. The work got done. Ok? I hope you guys are enjoying it
226:26 Ok? I hope you guys are enjoying it In questioning the. Let's go to the next question
226:28 In questioning the. Let's go to the next question Let's go. Okay, now for the next type.
226:29 Let's go. Okay, now for the next type. There are three questions. Ok? Next Type K
226:32 There are three questions. Ok? Next Type K There are three questions. We will do all three together.
226:34 There are three questions. We will do all three together. pay attention. How to ask the three first
226:36 pay attention. How to ask the three first Is it brother? one this
226:39 Is it brother? one this And what is this, all three are the same methods.
226:42 And what is this, all three are the same methods. Can't you see it? once again once again
226:44 Can't you see it? once again once again Look from. Ok? This one 1 2 3 1 2 3
226:48 Look from. Ok? This one 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 Okay? nowhere
226:53 1 2 3 1 2 3 1 2 3 1 2 3 Okay? nowhere It is not the same question anywhere. In such questions
226:56 It is not the same question anywhere. In such questions What is the plan? Teach at once and
226:58 What is the plan? Teach at once and A question from this also came in CBSE 2025.
227:01 A question from this also came in CBSE 2025. Ok? Pay attention first. what to do here
227:04 Ok? Pay attention first. what to do here Pay? What is there to do here? Ok? Attention
227:07 Pay? What is there to do here? Ok? Attention Give. Isn't it? Yes. He was wandering around a bit
227:09 Give. Isn't it? Yes. He was wandering around a bit Is. Anyway, let's go. So what should you do friend
227:11 Is. Anyway, let's go. So what should you do friend Here? The denominator is not to be tampered with.
227:14 Here? The denominator is not to be tampered with. What did I say? Not to the denominator
227:16 What did I say? Not to the denominator Have to tease. The denominator is not to be tampered with.
227:18 Have to tease. The denominator is not to be tampered with. Focus. Ok? So not the denominator
227:21 Focus. Ok? So not the denominator I will tease you.
227:23 I will tease you. Ok? Ok boss. The forest above
227:26 Ok? Ok boss. The forest above I have to change it. Change the forest above
227:29 I have to change it. Change the forest above Have to do it. Don't mess with the denominator. Above
227:31 Have to do it. Don't mess with the denominator. Above The one above has to be changed. Why do I tell
227:34 The one above has to be changed. Why do I tell Am. You all know that sec² - tan² theta
227:40 Am. You all know that sec² - tan² theta There is a forest. Yes or no. So instead of one, you get four –
227:46 There is a forest. Yes or no. So instead of one, you get four – You can write 3. 5 instead of 1 - 4 instead of 1
227:49 You can write 3. 5 instead of 1 - 4 instead of 1 100 - 99, instead of 1, 3 - 2, then instead of 1, you
227:53 100 - 99, instead of 1, 3 - 2, then instead of 1, you You can also write sec² - tan². That's what you're here for
227:56 You can also write sec² - tan². That's what you're here for You will write on Then see what the benefits are.
227:57 You will write on Then see what the benefits are. Is. So tan + sec left hand side attention
228:01 Is. So tan + sec left hand side attention Give. tan + sec If I sec Let tan + sec
228:04 Give. tan + sec If I sec Let tan + sec Just write sec and leave it. tan theta
228:08 Just write sec and leave it. tan theta + sec theta. Ok? pay attention. Minus One
228:11 + sec theta. Ok? pay attention. Minus One sec² theta - tan² theta instead of 1
228:18 sec² theta - tan² theta instead of 1 Don't make a mistake. If instead of one term there are two
228:21 Don't make a mistake. If instead of one term there are two Always use brackets when writing things.
228:24 Always use brackets when writing things. Ok? Divided by divided by
228:27 Ok? Divided by divided by Denominator. You guys will keep writing yourselves.
228:30 Denominator. You guys will keep writing yourselves. I said I don't want to change. Ok? Now
228:32 I said I don't want to change. Ok? Now See what benefit is being gained? The advantage is that
228:35 See what benefit is being gained? The advantage is that tan theta + sec theta is this. minus a² -
228:41 tan theta + sec theta is this. minus a² - What is b²? a² - b² is a + b
228:48 What is b²? a² - b² is a + b a + b
228:51 a + b * a - b is what happens. Answer very soon
228:55 * a - b is what happens. Answer very soon Will go. Don't worry. Ok? Just focus.
228:59 Will go. Don't worry. Ok? Just focus. Ok? pay attention. Ok? Now one thing
229:01 Ok? pay attention. Ok? Now one thing See.
229:03 See. The thing is that one term is this and the other is this.
229:07 The thing is that one term is this and the other is this. Term. Do you see anything common between the two?
229:08 Term. Do you see anything common between the two? Is? Is there anything similar between the two, brother? One Pocket
229:11 Is? Is there anything similar between the two, brother? One Pocket What is this one pocket? Is there anything in both?
229:13 What is this one pocket? Is there anything in both? Is it beans? next to this sec + tan oh tan + sec
229:16 Is it beans? next to this sec + tan oh tan + sec Say. Say sec + tan is the same thing. Its
229:18 Say. Say sec + tan is the same thing. Its tan + sec has tan + sec so
229:21 tan + sec has tan + sec so Why not take tan + sec out of both?
229:24 Why not take tan + sec out of both? Should be removed. Get kicked out of both.
229:26 Should be removed. Get kicked out of both. Get kicked out of both. Now just look
229:28 Get kicked out of both. Now just look What happened? tan theta + sec theta if I
229:33 What happened? tan theta + sec theta if I I will take it out. So look what's inside
229:35 I will take it out. So look what's inside Used to be. From here tan + sec went out. Outside
229:39 Used to be. From here tan + sec went out. Outside If Gaya goes out, the forest will be saved.
229:43 If Gaya goes out, the forest will be saved. Minus
229:44 Minus From here tan + sec goes out. these outside
229:47 From here tan + sec goes out. these outside If he goes out, what will be left? sec - tan
229:50 If he goes out, what will be left? sec - tan Just put the bracket on. This is your remaining sec theta
229:56 Just put the bracket on. This is your remaining sec theta - tan theta divided by the denominator. One
230:00 - tan theta divided by the denominator. One Let me tell you again what happened?
230:03 Let me tell you again what happened? tan + sec multiplied by one equals tan
230:06 tan + sec multiplied by one equals tan + sec will be formed. tan + sec go into it
230:09 + sec will be formed. tan + sec go into it Multiply then sec - tan tan + sec sec -
230:13 Multiply then sec - tan tan + sec sec - This will become tan tan + sec. Ok? Now enough
230:16 This will become tan tan + sec. Ok? Now enough The answer has come. Look how, look how? Ok?
230:20 The answer has come. Look how, look how? Ok? tan + sec
230:23 tan + sec This is your tan + sec, pay attention. tan + sec
230:26 This is your tan + sec, pay attention. tan + sec Ok? And what is there here? what's inside
230:28 Ok? And what is there here? what's inside Is? Put this bracket of yours here. Inside
230:31 Is? Put this bracket of yours here. Inside What's coming? Let's do a little bit like this
230:33 What's coming? Let's do a little bit like this This. tan theta
230:37 This. tan theta + sec theta what is coming in? 1 - sec +
230:41 + sec theta what is coming in? 1 - sec + tan 1
230:43 tan 1 - sec + tan now the denominator is one times
230:47 - sec + tan now the denominator is one times I will write it completely. You will understand that I
230:49 I will write it completely. You will understand that I Why is he refusing to change the denominator?
230:51 Why is he refusing to change the denominator? Was. what's down? tan - sec + 1 tan -
230:55 Was. what's down? tan - sec + 1 tan - sec + 1 tanθ - sec theta + 1 okay?
231:01 sec + 1 tanθ - sec theta + 1 okay? Friends, if you look carefully,
231:04 Friends, if you look carefully, tan + tan - sec - sec +1 +1
231:09 tan + tan - sec - sec +1 +1 again + tan + tan - sec - sec +1 + 1
231:15 again + tan + tan - sec - sec +1 + 1 The whole thing will be cut off by this. Any
231:18 The whole thing will be cut off by this. Any Beware, don't do this Chinese match. which one is this
231:21 Beware, don't do this Chinese match. which one is this Wali that this one + 1 + 1 from - sec - sec
231:25 Wali that this one + 1 + 1 from - sec - sec Then I could have cut it like this with +10 +10.
231:28 Then I could have cut it like this with +10 +10. How can this change from minus minus to plus plus
231:31 How can this change from minus minus to plus plus From S S From E E From C It can also be cut like this
231:36 From S S From E E From C It can also be cut like this It was like if you were cutting like that then
231:38 It was like if you were cutting like that then This is not to be done. You think that the one who
231:41 This is not to be done. You think that the one who The value of the whole thing will come, that is the value of this whole thing.
231:43 The value of the whole thing will come, that is the value of this whole thing. What does it mean to say the value of? that this is complete
231:46 What does it mean to say the value of? that this is complete This whole thing will be cut off.
231:49 This whole thing will be cut off. Ok? So what's left? only and only tan
231:52 Ok? So what's left? only and only tan theta + sec theta. And what do you want?
231:55 theta + sec theta. And what do you want? If you want sin cos then enter sin cos
231:57 If you want sin cos then enter sin cos Convert it. So here you go, sinθ/
232:02 Convert it. So here you go, sinθ/ cos theta is your 1 / cos theta LCM
232:06 cos theta is your 1 / cos theta LCM No need to take it because the denominator is the same
232:09 No need to take it because the denominator is the same Is. So sinθ + 1 / cos theta sinθ + 1 /
232:13 Is. So sinθ + 1 / cos theta sinθ + 1 / cos theta has proven
232:16 cos theta has proven You have to ask this question in this manner.
232:18 You have to ask this question in this manner. Now, as tan sec was given here, then this
232:22 Now, as tan sec was given here, then this Change to sec² - tan². CBSE 2025
232:26 Change to sec² - tan². CBSE 2025 This question of CBSE 2025
232:31 This question of CBSE 2025 Ditto question, this time why do you call the forest
232:34 Ditto question, this time why do you call the forest Will you change? This time you are in the forest.
232:37 Will you change? This time you are in the forest. Will you change? cosec²
232:40 Will you change? cosec² a - cot² a and the same thing, the same old
232:47 a - cot² a and the same thing, the same old Things have to be followed. a cosec² - cot² then
232:51 Things have to be followed. a cosec² - cot² then cosec + cot cosec - cot cosec + cot
232:54 cosec + cot cosec - cot cosec + cot cosec + cot common this whole cut from the whole
232:57 cosec + cot common this whole cut from the whole Will go. Then by converting it to sin cos you get this
233:00 Will go. Then by converting it to sin cos you get this You will get the answer. Ditto as it is
233:02 You will get the answer. Ditto as it is You have to ask this question to yourself. Ok
233:05 You have to ask this question to yourself. Ok No? It has to be done. It is a similar question.
233:08 No? It has to be done. It is a similar question. I have to try it. Try what to do
233:10 I have to try it. Try what to do Will go. Now here it's just a little bit different. Is
233:13 Will go. Now here it's just a little bit different. Is Same question. Just what is different? Hear
233:15 Same question. Just what is different? Hear be careful. 1 second patience is what's different
233:21 be careful. 1 second patience is what's different Here when you change this one to sec² -
233:24 Here when you change this one to sec² - In tan², the identity a² - b² is used. a
233:28 In tan², the identity a² - b² is used. a - b a + b
233:31 - b a + b When you change one here to cosec² -
233:35 When you change one here to cosec² - cot² then a² - b² a - b a + b
233:40 cot² then a² - b² a - b a + b There is identity. But here's the problem
233:43 There is identity. But here's the problem If you write one here, sin² a +
233:48 If you write one here, sin² a + cos² a then the identity a² + b² will apply which
233:53 cos² a then the identity a² + b² will apply which That there will be a different identity.
233:56 That there will be a different identity. The identity of a² - b² is not found. a²
234:01 The identity of a² - b² is not found. a² - Identity of b² is not found. So now
234:04 - Identity of b² is not found. So now What should I do? You have to answer this particular question
234:07 What should I do? You have to answer this particular question What do I have to do? I tell you. Listen
234:11 What do I have to do? I tell you. Listen I am speaking again. You can write this as sin² +
234:13 I am speaking again. You can write this as sin² + You will change it to cos². no point.
234:16 You will change it to cos². no point. Because sin² + cos² changes to + cos²
234:19 Because sin² + cos² changes to + cos² Used to be. If there is a change in sin² - cos²
234:23 Used to be. If there is a change in sin² - cos² Would. Brother, you will talk about identity. Now
234:25 Would. Brother, you will talk about identity. Now Write sin² - cos² instead. hey that
234:27 Write sin² - cos² instead. hey that There is no identity. sin² + instead of one
234:31 There is no identity. sin² + instead of one You can write cos². Identity of a² - b²
234:35 You can write cos². Identity of a² - b² I can't seem to. If the identity is not visible
234:37 I can't seem to. If the identity is not visible Then that denominator doesn't cancel the denominator.
234:39 Then that denominator doesn't cancel the denominator. will be. So here I tell you what to do.
234:41 will be. So here I tell you what to do. Am. Above
234:44 Am. Above above sin theta
234:46 above sin theta - cos theta + 1
234:49 - cos theta + 1 Divide the whole by cos theta.
234:53 Divide the whole by cos theta. And the same thing below. Brother, if you are above someone
234:56 And the same thing below. Brother, if you are above someone If you are dividing by cheese then the bottom is also the same
234:59 If you are dividing by cheese then the bottom is also the same You can divide it by cheese. could do that
235:01 You can divide it by cheese. could do that I am here. If you change the numerator from to
235:03 I am here. If you change the numerator from to If you are dividing, divide the denominator by two.
235:05 If you are dividing, divide the denominator by two. Divide it by . What is the benefit of just one thing?
235:07 Divide it by . What is the benefit of just one thing? sin / cos
235:10 sin / cos tan cos 1 / cos 1
235:15 tan cos 1 / cos 1 sec divided by sin / cos
235:20 sec divided by sin / cos tan cos / cos 1 / cos 1 / cos sec Now you
235:28 tan cos / cos 1 / cos 1 / cos sec Now you Look, this has become the first question. These
235:31 Look, this has become the first question. These The first one became the question. tan - 1 +
235:34 The first one became the question. tan - 1 + Write sec here.
235:37 Write sec here. tan - 1 + sec tan - sec + 1
235:43 tan - 1 + sec tan - sec + 1 tan - sec + 1 will you do? The same thing in this forest
235:48 tan - sec + 1 will you do? The same thing in this forest change to sec² theta - tan² theta
235:55 change to sec² theta - tan² theta In. The exact same old question
235:57 In. The exact same old question Will go. Hashtag to do at home. Ok? These
236:02 Will go. Hashtag to do at home. Ok? These Everyone understood why this forest was not
236:04 Everyone understood why this forest was not Get it changed? sin² + cos² because a² + b²
236:09 Get it changed? sin² + cos² because a² + b² It is coming. I want a² - b². And that's when
236:12 It is coming. I want a² - b². And that's when It will come when you convert it into sec tan or cosec
236:15 It will come when you convert it into sec tan or cosec Change into cot. ok telling you one thing
236:18 Change into cot. ok telling you one thing Am. If cosec cot cosec cot
236:20 Am. If cosec cot cosec cot You should have brought cosec cot. So you don't know cos
236:24 You should have brought cosec cot. So you don't know cos Divide by sin. Then
236:26 Divide by sin. Then Because the advantage is that sin / sin 1 cos
236:29 Because the advantage is that sin / sin 1 cos / sin cot 1 / sin cosec cosec cot comes.
236:35 / sin cot 1 / sin cosec cosec cot comes. Ok? Ok? So this is your type.
236:38 Ok? Ok? So this is your type. The questions also end here.
236:40 The questions also end here. Are. Now the next very important thing
236:43 Are. Now the next very important thing Listen carefully. Very variant things that I learned
236:46 Listen carefully. Very variant things that I learned I have been. Focus on this thing for 5 minutes. Correct
236:49 I have been. Focus on this thing for 5 minutes. Correct Is? You know that sec² theta
236:53 Is? You know that sec² theta - tan² theta is 1. Ok? concept
236:58 - tan² theta is 1. Ok? concept To remember the hashtag ctr concept to
237:01 To remember the hashtag ctr concept to Remember. sec² theta - tan² theta is 1.
237:04 Remember. sec² theta - tan² theta is 1. Can I use the identity a² - b² here?
237:07 Can I use the identity a² - b² here? I can say by approximation that sec - tan *
237:11 I can say by approximation that sec - tan * sec + tan is equal to 1. So here you
237:16 sec + tan is equal to 1. So here you It should be understood that you can convert sec + tan
237:19 It should be understood that you can convert sec + tan You can write 1 / sec - tan and sec - tan
237:24 You can write 1 / sec - tan and sec - tan to y and sec - tan to y 1 / sec + tan
237:29 to y and sec - tan to y 1 / sec + tan You can write. This is an important matter. These
237:33 You can write. This is an important matter. These This is an important matter. too much
237:36 This is an important matter. too much Important thing. I am explaining. If
237:38 Important thing. I am explaining. If If you don't understand then don't worry. Little
237:40 If you don't understand then don't worry. Little Try to understand. Let me tell you one more thing
237:42 Try to understand. Let me tell you one more thing Am. If you know cosec² theta -
237:47 Am. If you know cosec² theta - cot² theta is 1 then a² - b² means a
237:53 cot² theta is 1 then a² - b² means a + b
237:56 + b * a
237:59 * a - b equals one. What you mean to say is that you
238:03 - b equals one. What you mean to say is that you cosec theta
238:06 cosec theta + cot theta to 1 /
238:10 + cot theta to 1 / cosec theta - cot theta and
238:16 cosec theta - cot theta and cosec theta - cot theta is 1 / cosec you
238:23 cosec theta - cot theta is 1 / cosec you you can write theta + cot theta what are the
238:26 you can write theta + cot theta what are the The Last Few Things in the Chapter That Remain
238:28 The Last Few Things in the Chapter That Remain That's what I'm teaching you, okay? In this
238:31 That's what I'm teaching you, okay? In this You can also put a star. Couldn't understand anything
238:34 You can also put a star. Couldn't understand anything Brother. Please explain it again. I am explaining.
238:36 Brother. Please explain it again. I am explaining. Why are you taking tension? Look here. Ok?
238:40 Why are you taking tension? Look here. Ok? Look what I am trying to say. Correct
238:42 Look what I am trying to say. Correct Is? Look here. Here you go. You know this
238:46 Is? Look here. Here you go. You know this Is. This will mean this. So look at it
238:48 Is. This will mean this. So look at it If sec + tan is right here. sec - tan to
238:52 If sec + tan is right here. sec - tan to Take it down. So the value of sec + tan is 1 /
238:55 Take it down. So the value of sec + tan is 1 / sec - tan. 1 / sec instead of sec + tan -
238:58 sec - tan. 1 / sec instead of sec + tan - tan. 1 / sec - tan instead of sec + tan and
239:01 tan. 1 / sec - tan instead of sec + tan and sec - tan is replaced by 1 / sec + tan similarly
239:05 sec - tan is replaced by 1 / sec + tan similarly Here instead of cosec + cot, we get 1 / cosec -
239:08 Here instead of cosec + cot, we get 1 / cosec - cot cosec - cot instead of 1 / cosec + cot
239:11 cot cosec - cot instead of 1 / cosec + cot You can write it if you look at it like this.
239:15 You can write it if you look at it like this. If you want to listen, then accept that you want to listen for five minutes.
239:18 If you want to listen, then accept that you want to listen for five minutes. This will prove that you got into the question.
239:20 This will prove that you got into the question. Prove that Prove to pay attention Prove the
239:23 Prove that Prove to pay attention Prove the following
239:25 following Prove the Following is here to prove you
239:29 Prove the Following is here to prove you Prove that sec theta + tan theta
239:33 Prove that sec theta + tan theta is equal to 1 / sec theta - tan theta.
239:38 is equal to 1 / sec theta - tan theta. How will you prove it? I will tell you here. You
239:41 How will you prove it? I will tell you here. You Left hand side raised. sec + tan sec +
239:46 Left hand side raised. sec + tan sec + Tan picked up. What should you do now? in sec + tan
239:49 Tan picked up. What should you do now? in sec + tan Multiply sec - tan and sec - tan by itself
239:53 Multiply sec - tan and sec - tan by itself Divide it. You can do this. Now sec
239:56 Divide it. You can do this. Now sec from + tan in sec - tan sec - tan
239:59 from + tan in sec - tan sec - tan You can multiply and divide. What is the benefit
240:01 You can multiply and divide. What is the benefit Happened? a + b a - b so this gives sec² - tan²
240:05 Happened? a + b a - b so this gives sec² - tan² and below sec - tan sec² - tan² is 1.
240:09 and below sec - tan sec² - tan² is 1. So 1 - sec - tan is what you wanted.
240:12 So 1 - sec - tan is what you wanted. Went. So you have divided sec + tan by sec + tan = 1
240:16 Went. So you have divided sec + tan by sec + tan = 1 / sec - proved in tan.
240:20 / sec - proved in tan. Ok? Did you understand this thing? Very
240:24 Ok? Did you understand this thing? Very It is an important thing. very important thing
240:26 It is an important thing. very important thing that sec + tan is equal to 1 / sec - tan
240:29 that sec + tan is equal to 1 / sec - tan It happens. sec - tan 1 / sec + tan
240:32 It happens. sec - tan 1 / sec + tan It is equal. cosec + cot 1 / cosec -
240:34 It is equal. cosec + cot 1 / cosec - is equal to cot. cosec - cot 1 /
240:37 is equal to cot. cosec - cot 1 / is equal to cosec + tan. I understood
240:40 is equal to cosec + tan. I understood To you? Surely Badu. Let's move ahead. Come very much
240:45 To you? Surely Badu. Let's move ahead. Come very much Lovely question. Very nice question. such questions
240:48 Lovely question. Very nice question. such questions were asked earlier. They are not asked anymore. But
240:50 were asked earlier. They are not asked anymore. But You never know. Let's try it. What lyrics
240:53 You never know. Let's try it. What lyrics Used to be? sec theta + tan theta is equal to P
240:56 Used to be? sec theta + tan theta is equal to P Is. sec theta + tan theta is equal to P.
240:59 Is. sec theta + tan theta is equal to P. Ok? I told you to obtain the value of sec
241:02 Ok? I told you to obtain the value of sec theta tan theta and sin theta in terms of
241:06 theta tan theta and sin theta in terms of P. What have you been asked to remove? To you
241:09 P. What have you been asked to remove? To you We need to find the value of sec theta. tan theta
241:12 We need to find the value of sec theta. tan theta I have to take it out. We have to find sin theta. p
241:14 I have to take it out. We have to find sin theta. p In terms of. Meaning when you sec theta
241:16 In terms of. Meaning when you sec theta If you take it out, some of it will come in the form of p.
241:18 If you take it out, some of it will come in the form of p. When you find tan theta, you'll get something like p
241:20 When you find tan theta, you'll get something like p It will come in the form. when you find sin theta
241:22 It will come in the form. when you find sin theta So something will come in the form of p. Ok? qd
241:27 So something will come in the form of p. Ok? qd Let me help you with this question.
241:30 Let me help you with this question. Will be needed. Be patient. Ok? So
241:32 Will be needed. Be patient. Ok? So Listen first of all friend. I will make it very easy
241:36 Listen first of all friend. I will make it very easy For you. sec + tan gave you p.
241:38 For you. sec + tan gave you p. It should automatically come to your mind.
241:40 It should automatically come to your mind. What is sec - tan? sec - tan what
241:44 What is sec - tan? sec - tan what It happens? 1/sec + tan
241:48 It happens? 1/sec + tan 1 / sec + tan brother what is sec - tan
241:52 1 / sec + tan brother what is sec - tan Is? 1 / sec + tan sec + tan means p then
241:55 Is? 1 / sec + tan sec + tan means p then sec + tan sec - tan 1 / p will come out. I
241:59 sec + tan sec - tan 1 / p will come out. I I want to say this. So this is an equation
242:01 I want to say this. So this is an equation Secondly, did you understand this? Again
242:05 Secondly, did you understand this? Again Let me tell you. equal to sec + tan p. sec-
242:09 Let me tell you. equal to sec + tan p. sec- equal to tan 1 / p. Why so? sec - tan
242:12 equal to tan 1 / p. Why so? sec - tan What happens? I just taught it. 1/sec + tan
242:14 What happens? I just taught it. 1/sec + tan So 1 / sec + tan whose value is p. Now
242:18 So 1 / sec + tan whose value is p. Now You just add these two equations once.
242:20 You just add these two equations once. And minus one more time. sec will get tan
242:22 And minus one more time. sec will get tan The matter will be resolved. If you both understand the equation
242:24 The matter will be resolved. If you both understand the equation Look at. Hey, don't be afraid. this x this x this y
242:27 Look at. Hey, don't be afraid. this x this x this y Imagine this like this. If both of you
242:29 Imagine this like this. If both of you If you add the equation, what will happen?
242:31 If you add the equation, what will happen? sec theta
242:33 sec theta + tanθ = p sec theta
242:38 + tanθ = p sec theta - tanθ = 1 / p plus sin then change
242:42 - tanθ = 1 / p plus sin then change Otherwise, sec + sec is 2sec theta +
242:46 Otherwise, sec + sec is 2sec theta + tan - tan cancels out, this is your p + 1 / p here.
242:50 tan - tan cancels out, this is your p + 1 / p here. So you have to take the LCM of sec theta
242:53 So you have to take the LCM of sec theta 2sec theta will return the value p²
242:57 2sec theta will return the value p² + 1 / p means sec theta you have come
243:02 + 1 / p means sec theta you have come p² + 1/2p
243:05 p² + 1/2p Look, your sec theta has come, which you
243:07 Look, your sec theta has come, which you Was Needed. Now subtract both the equations.
243:10 Was Needed. Now subtract both the equations. Two or one times. If you solve both equations
243:12 Two or one times. If you solve both equations If you minus it, see what will come out. If
243:14 If you minus it, see what will come out. If You minus both
243:17 You minus both I don't do it directly. Let secθ +
243:20 I don't do it directly. Let secθ + tanθ p equals secθ
243:25 tanθ p equals secθ - tanθ equals 1/p tan if u minus
243:29 - tanθ equals 1/p tan if u minus If you are doing the equation then this is the minus of the plus.
243:32 If you are doing the equation then this is the minus of the plus. This minus plus this plus minus so sec
243:35 This minus plus this plus minus so sec - sec cancels + tan + tan 2 tan
243:40 - sec cancels + tan + tan 2 tan If you take the LCM of theta p - 1 / p - 1 / p
243:45 If you take the LCM of theta p - 1 / p - 1 / p Same thing 2tanθ = p² − 1 / p so tanθ
243:51 Same thing 2tanθ = p² − 1 / p so tanθ The value arrived at is p² - 1/2p
243:58 The value arrived at is p² - 1/2p End. Ok? So tan theta also comes, sec
244:01 End. Ok? So tan theta also comes, sec Theta also came. What to remove now? sin
244:03 Theta also came. What to remove now? sin Theta. Now how will this sin theta be calculated?
244:06 Theta. Now how will this sin theta be calculated? Should I tell you? Direct. You don't do anything. you tan
244:11 Should I tell you? Direct. You don't do anything. you tan Theta or look at it like this. know sin theta
244:15 Theta or look at it like this. know sin theta What happens? Now you don't know this
244:17 What happens? Now you don't know this will be. But this question will reveal that
244:20 will be. But this question will reveal that sin theta is tanθ / sec theta. As such
244:23 sin theta is tanθ / sec theta. As such Why? see tan theta means sin / cos
244:27 Why? see tan theta means sin / cos sec means 1 / cos cos divided by cos one
244:30 sec means 1 / cos cos divided by cos one Sin saved. I am telling you again. Meaning of tan
244:33 Sin saved. I am telling you again. Meaning of tan sin / cos sec means 1 / cos sec to cos
244:36 sin / cos sec means 1 / cos sec to cos The sin is saved. So sin theta is converted to tan / sec
244:40 The sin is saved. So sin theta is converted to tan / sec You can write tan / sec. So if you sin
244:43 You can write tan / sec. So if you sin In this question, you have to find theta, so tan
244:46 In this question, you have to find theta, so tan What is the value of theta? p² - 1 / 2p p² -
244:52 What is the value of theta? p² - 1 / 2p p² - What is the value of 1/2p and sec theta? p²
244:57 What is the value of 1/2p and sec theta? p² + 1/2p Pay attention. p² + 1 / 2p then 2p
245:02 + 1/2p Pay attention. p² + 1 / 2p then 2p 2p was cut from. The direct answer to sinθ is
245:06 2p was cut from. The direct answer to sinθ is Given p² - 1 / p² + 1
245:11 Given p² - 1 / p² + 1 I'm moving a little faster now.
245:14 I'm moving a little faster now. Because whoever is looking till here now
245:16 Because whoever is looking till here now You must be understanding everything. Correct
245:18 You must be understanding everything. Correct Is? Is it clear? Do you understand? My
245:21 Is? Is it clear? Do you understand? My The energy did not go down. not even yours
245:23 The energy did not go down. not even yours Should be. I am getting it done in full
245:25 Should be. I am getting it done in full Am. Better than this one shot you will get the whole YouTube
245:28 Am. Better than this one shot you will get the whole YouTube It will not be found in the history of. This is mine
245:29 It will not be found in the history of. This is mine It is guaranteed. Ok? Is it clear? every one
245:33 It is guaranteed. Ok? Is it clear? every one You are learning something new in the question. Note
245:36 You are learning something new in the question. Note Keep doing it. It is important to make notes.
245:40 Keep doing it. It is important to make notes. Ok? So, that's it, boss. Ok?
245:42 Ok? So, that's it, boss. Ok? Similarly, you have a question for your family.
245:46 Similarly, you have a question for your family. I am giving it for you. GPK has to be done. Hint
245:50 I am giving it for you. GPK has to be done. Hint What is? This is the hint. The hint is that
245:53 What is? This is the hint. The hint is that You should know that cosec theta--
245:57 You should know that cosec theta-- cot theta will be equal to 1 / p. And one more
246:01 cot theta will be equal to 1 / p. And one more I'm hinting that cos theta is cos
246:05 I'm hinting that cos theta is cos theta is cot theta.
246:10 theta is cot theta. / cosec theta
246:13 / cosec theta Ok? Similarly, the question is a similar point.
246:16 Ok? Similarly, the question is a similar point. But. Ok? Do it and keep it. tell me what you do
246:18 But. Ok? Do it and keep it. tell me what you do Tell me that I have done it brother. Okay, right? CBSE
246:21 Tell me that I have done it brother. Okay, right? CBSE I have had a question many times. very much
246:23 I have had a question many times. very much Simple question. Ok? CBSE has a lot of
246:25 Simple question. Ok? CBSE has a lot of The bar has arrived. I will direct it
246:27 The bar has arrived. I will direct it Ours.
246:29 Ours. Now I told you that some questions would be like this
246:32 Now I told you that some questions would be like this in which both sides have to be solved
246:34 in which both sides have to be solved Is. This is one of those questions. how know
246:36 Is. This is one of those questions. how know walked? If you pay attention, somewhere both
246:39 walked? If you pay attention, somewhere both Only the side seams are visible. nowhere
246:40 Only the side seams are visible. nowhere At some places both sides appear to be the same.
246:42 At some places both sides appear to be the same. Both sides have to be solved. and the rest if
246:44 Both sides have to be solved. and the rest if What to do if you don't understand directly?
246:46 What to do if you don't understand directly? Is? Solve one side. More Solve
246:49 Is? Solve one side. More Solve You won't be able to do it. So in that case the other side
246:51 You won't be able to do it. So in that case the other side Will have to solve it too. Now you just now
246:53 Will have to solve it too. Now you just now So I learned it. I just learned it. 1 / cosec -
246:57 So I learned it. I just learned it. 1 / cosec - What is cot? cosec + cot. Yes or no.
247:00 What is cot? cosec + cot. Yes or no. I just learned it brother. This step is the first
247:03 I just learned it brother. This step is the first bring down. After that second step 1/
247:06 bring down. After that second step 1/ What is cosec - cot? I just taught
247:08 What is cosec - cot? I just taught cosec + cot brother cosec + cot is 1 /
247:13 cosec + cot brother cosec + cot is 1 / cosec - cot then 1 / cosec - cosec + cot
247:17 cosec - cot then 1 / cosec - cosec + cot What is minus 1 / sin a? cosec a
247:21 What is minus 1 / sin a? cosec a What is the benefit? cosec of plus cosec of - cosec
247:24 What is the benefit? cosec of plus cosec of - cosec Went. cot a left. friend now this from cot a
247:28 Went. cot a left. friend now this from cot a How do I bring it all? It seems like an impossible task
247:31 How do I bring it all? It seems like an impossible task Used to be. So we have to stop here. This is yours
247:33 Used to be. So we have to stop here. This is yours LHS. Now look at the RHS. Now look at the RHS.
247:38 LHS. Now look at the RHS. Now look at the RHS. What is 1 / sin a? First of all this is
247:40 What is 1 / sin a? First of all this is Take the step down. Then what is 1 / sin a
247:43 Take the step down. Then what is 1 / sin a Is? 1 / sin a cosec a minus bracket 1 /
247:48 Is? 1 / sin a cosec a minus bracket 1 / What is cosec + cot?
247:51 What is cosec + cot? cosec - cot how much did this cost you? This comes
247:55 cosec - cot how much did this cost you? This comes Gone is your cosec a
247:58 Gone is your cosec a - cosec a
248:00 - cosec a + cot a + cosec - cosec went right hand
248:05 + cot a + cosec - cosec went right hand If your side also comes then just sin
248:10 If your side also comes then just sin Left Hand Side Equ Right Hand Side Equ
248:14 Left Hand Side Equ Right Hand Side Equ cot a
248:17 cot a He proved it was a matter of choice for a select few.
248:20 He proved it was a matter of choice for a select few. You have to solve both sides of the questions.
248:22 You have to solve both sides of the questions. It happens, right? Come on, next. on that
248:26 It happens, right? Come on, next. on that Let's go. Very simple question. very much
248:28 Let's go. Very simple question. very much Simple question. Ok? Now something like this
248:31 Simple question. Ok? Now something like this Where I say something like this
248:33 Where I say something like this I am speaking. sin theta + cos theta p
248:36 I am speaking. sin theta + cos theta p Equal to. sec theta + cosec theta of q
248:39 Equal to. sec theta + cosec theta of q Equal. Meaning basically the value of p is given. q
248:42 Equal. Meaning basically the value of p is given. q The value of is given. Show That Ya Show That Ya
248:46 The value of is given. Show That Ya Show That Ya Meaning you are not directly saying that LHS
248:48 Meaning you are not directly saying that LHS Make the RHS equal. saying in a roundabout way that
248:51 Make the RHS equal. saying in a roundabout way that Just prove it. Meaning, what should I prove? q
248:54 Just prove it. Meaning, what should I prove? q * Try proving that p² - 1 = 2p. It will be good if
248:58 * Try proving that p² - 1 = 2p. It will be good if the value of q instead of q so instead of q I
249:01 the value of q instead of q so instead of q I written sec theta
249:05 written sec theta + cosec theta these instead of q then p instead of p
249:10 + cosec theta these instead of q then p instead of p instead of p sin theta + cos theta then p
249:13 instead of p sin theta + cos theta then p In place of
249:15 In place of sin theta + cos theta p instead of sin theta +
249:18 sin theta + cos theta p instead of sin theta + cos theta its squared - 1
249:22 cos theta its squared - 1 okay right okay this LHS I
249:26 okay right okay this LHS I I picked up the LHS. I picked up the LHS. Ok
249:29 I picked up the LHS. I picked up the LHS. Ok No? let us see. Let's solve it. So this
249:32 No? let us see. Let's solve it. So this So it is understood that in boss sin cos
249:35 So it is understood that in boss sin cos Let's change all the things. So this is your
249:37 Let's change all the things. So this is your 1 / cos this is your 1 / sin look here. sin +
249:41 1 / cos this is your 1 / sin look here. sin + cos² is sin² + cos² + 2sin cos - 1
249:48 cos² is sin² + cos² + 2sin cos - 1 Correct? a + b whole square. look here now
249:51 Correct? a + b whole square. look here now LCM to LCM then cos sin LCM cos
249:53 LCM to LCM then cos sin LCM cos cos left sin then sin 1 sin sins left cos then
249:56 cos left sin then sin 1 sin sins left cos then sin + cos what comes here minus 1
249:59 sin + cos what comes here minus 1 Sorry, 1 + 2sin cos - 1 + 1 went to -1.
250:03 Sorry, 1 + 2sin cos - 1 + 1 went to -1. This is your remaining sin + cos cos sin * 2sin cos
250:09 This is your remaining sin + cos cos sin * 2sin cos sin cos went from sin cos to sin cos so this is what you got
250:12 sin cos went from sin cos to sin cos so this is what you got 2 * sin + cos ok now what was sin + cos
250:18 2 * sin + cos ok now what was sin + cos So this is equal to your 2p.
250:22 So this is equal to your 2p. This is what had to be proved. This is what you have to prove
250:25 This is what had to be proved. This is what you have to prove Was. Equ
250:28 Was. Equ RHS Hens Proven. tell me once again
250:31 RHS Hens Proven. tell me once again I have been. once again once again okay
250:34 I have been. once again once again okay Is? I put this instead of nothing q. of p
250:38 Is? I put this instead of nothing q. of p This was kept in place. Ok? So instead of q, this
250:41 This was kept in place. Ok? So instead of q, this This value instead of the value p. a + b² then a²
250:46 This value instead of the value p. a + b² then a² + b² + 2ab sec + cosec cos sin cos
250:49 + b² + 2ab sec + cosec cos sin cos I think things are easy so 1 / cos 1 / sin
250:52 I think things are easy so 1 / cos 1 / sin If we take the LCM, we get sin² + cos² 1 +
250:55 If we take the LCM, we get sin² + cos² 1 + 1 to -1 went from +1 to -1 2sin cos left
250:59 1 to -1 went from +1 to -1 2sin cos left sin cos sin cos goes to 2 * sin + cos 2 *
251:04 sin cos sin cos goes to 2 * sin + cos 2 * sin + cos 2 * sin + cos you need to bring to 2p
251:07 sin + cos 2 * sin + cos you need to bring to 2p So you see 2, but you know that sin
251:10 So you see 2, but you know that sin + cos sin + cos p is equal to
251:15 + cos sin + cos p is equal to Ok.
251:16 Ok. Ok. Do you understand? I am enjoying it.
251:18 Ok. Do you understand? I am enjoying it. There is still a lot left, child. Ok. Patience
251:20 There is still a lot left, child. Ok. Patience Have to keep it. Let's take a very
251:23 Have to keep it. Let's take a very Lovely, very favorite question. Look at this like that
251:27 Lovely, very favorite question. Look at this like that This is actually RD Sharma's question. But this
251:30 This is actually RD Sharma's question. But this The question was asked by CBSE this year.
251:33 The question was asked by CBSE this year. Ditto ditto, same question, just a slight change.
251:36 Ditto ditto, same question, just a slight change. Had done it. First he does this and then he shows
251:38 Had done it. First he does this and then he shows Am. You will do that yourself. Ok? Come on what
251:41 Am. You will do that yourself. Ok? Come on what Are you speaking? tanθ + sinθ is equal to m.
251:45 Are you speaking? tanθ + sinθ is equal to m. Meaning basically the value of m is given and n
251:49 Meaning basically the value of m is given and n The value of is given. I told you to show that
251:51 The value of is given. I told you to show that m² - n² equals this. So the same thing that Boss m²
251:58 m² - n² equals this. So the same thing that Boss m² - m² is to be proved equal to 2 mn. 2 mn
252:02 - m² is to be proved equal to 2 mn. 2 mn Equal to. So, you would have put the values first.
252:04 Equal to. So, you would have put the values first. Are. Basically what do you have to prove?
252:06 Are. Basically what do you have to prove? tanθ
252:09 tanθ + sinθ
252:11 + sinθ Time Square - tanθ instead of n
252:16 Time Square - tanθ instead of n - sinθ²
252:18 - sinθ² = 2
252:21 = 2 Meaning
252:23 Meaning tanθ + sinθ
252:27 tanθ + sinθ and this tanθ -
252:32 and this tanθ - sinθ
252:33 sinθ This is what has to be proved. Nothing. m instead of m
252:36 This is what has to be proved. Nothing. m instead of m value of, n instead of n value of, m
252:38 value of, n instead of n value of, m The value of m in place of n, the value of n in place of n.
252:41 The value of m in place of n, the value of n in place of n. So you have to solve this and bring it. This
252:44 So you have to solve this and bring it. This I have to solve this and bring it. Ok? So a job
252:46 I have to solve this and bring it. Ok? So a job We do. Raise the left hand side.
252:50 We do. Raise the left hand side. Ok? Well, by the way, I understand one more thing.
252:52 Ok? Well, by the way, I understand one more thing. It must be coming that a + b * a - b a + b * a -
252:56 It must be coming that a + b * a - b a + b * a - This becomes b a² - b² i.e. tan² - sec².
253:00 This becomes b a² - b² i.e. tan² - sec². Ok? Ok? Let's solve it. So a
253:02 Ok? Ok? Let's solve it. So a + b² I told you a² + b² + 2ab
253:09 + b² I told you a² + b² + 2ab Ok? There should be no mistake. Minus here
253:12 Ok? There should be no mistake. Minus here but also a² + b² - 2ab
253:17 but also a² + b² - 2ab Ok? Okay, right? then tan²
253:21 Ok? Okay, right? then tan² + sec²
253:23 + sec² + 2tan
253:25 + 2tan - tan² - sin² sorry it is not sec it is sin +
253:29 - tan² - sin² sorry it is not sec it is sin + 2tan
253:31 2tan so + tan² - tan² + sin² - sin² 2 tan 2
253:36 so + tan² - tan² + sin² - sin² 2 tan 2 tan sin is here, your 4 tan 4 tan
253:42 tan sin is here, your 4 tan 4 tan What should I do now? There you have it, 4 tan sin.
253:46 What should I do now? There you have it, 4 tan sin. Friend, I don't get such confidence from anywhere.
253:48 Friend, I don't get such confidence from anywhere. I can't find the root of tan sin 4.
253:51 I can't find the root of tan sin 4. and also in tan + sin tan - sin
253:54 and also in tan + sin tan - sin If I change it, I'll leave it here.
253:56 If I change it, I'll leave it here. Give. Now I will solve the right hand side.
253:58 Give. Now I will solve the right hand side. What did I tell you? A select few
254:00 What did I tell you? A select few There are questions where both
254:02 There are questions where both Side problems have to be solved. That's this question
254:04 Side problems have to be solved. That's this question How did you understand that friend, where did you get 4* from?
254:07 How did you understand that friend, where did you get 4* from? tan * sin to the root of tan + sin
254:10 tan * sin to the root of tan + sin will change to tan - sin. Very
254:12 will change to tan - sin. Very It seems like a difficult task. So why not
254:14 It seems like a difficult task. So why not That should be simplified. I am not this
254:16 That should be simplified. I am not this He is saying that this cannot be done. But
254:18 He is saying that this cannot be done. But It is difficult. Why not simplify it?
254:20 It is difficult. Why not simplify it? We do. Come on. So when you simplify it
254:21 We do. Come on. So when you simplify it then I get 2 root 2 root a + b a - b
254:27 then I get 2 root 2 root a + b a - b a² - b² friend if you want to get this then remove the root
254:33 a² - b² friend if you want to get this then remove the root Will have to. When will the root be removed? When the Hole is Square
254:35 Will have to. When will the root be removed? When the Hole is Square Will come. How should I do it? How should I do it? How should I do it?
254:39 Will come. How should I do it? How should I do it? How should I do it? If you don't understand something, if you don't understand something, it's a sin
254:43 If you don't understand something, if you don't understand something, it's a sin cos do. Let's see what the benefit is
254:46 cos do. Let's see what the benefit is under root sin² cos² sin²
254:53 under root sin² cos² sin² We're okay so it made sense that if I
254:57 We're okay so it made sense that if I If I take sin² from above then it is 1 / cos² - 1
255:03 If I take sin² from above then it is 1 / cos² - 1 Ok? If you want to take LCM then 2 route meditation
255:05 Ok? If you want to take LCM then 2 route meditation Give sin² 1 - cos² / cos²
255:10 Give sin² 1 - cos² / cos² Yes, understand one thing, 2 root sin² / cos²
255:18 Yes, understand one thing, 2 root sin² / cos² 1 - cos² is sin²
255:21 1 - cos² is sin² Did you understand anything? Did you understand anything? sin² /
255:25 Did you understand anything? Did you understand anything? sin² / cos² because you need tan then sin² /
255:28 cos² because you need tan then sin² / cos² tan² sin²
255:31 cos² tan² sin² What was the benefit? The advantage is that 2
255:35 What was the benefit? The advantage is that 2 tan²
255:37 tan² In sin² multiplication then the roots give different
255:40 In sin² multiplication then the roots give different I can. Square root from square
255:41 I can. Square root from square Root so 2 tan sin answer is there.
255:46 Root so 2 tan sin answer is there. 1 second, did something go wrong?
255:49 1 second, did something go wrong? Did something go wrong? 1 sec 2 mn these 4
255:55 Did something go wrong? 1 sec 2 mn these 4 tan sin
255:57 tan sin 4 tan sin should come out. over here 4 tan sin
255:59 4 tan sin should come out. over here 4 tan sin Why are you not coming? a² - b² right? So
256:04 Why are you not coming? a² - b² right? So
