Inverse Trigonometric Functions | One Shot | #BounceBack Series | Unacademy Atoms | Nishant Vora

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In this JEE 2022 session, Nishant Vora Sir will be discussing Inverse Trigonometric Functions in One Shot for JEE Main & Advanced 2022. Here, Nishant Vora Sir solves various examples based on the topic of Inverse Trigonometric Functions for JEE Main & Advanced 2022. Nishant Vora Sir also shares his various preparation strategies which will help you to crack the JEE Main/NEET Exam. Watch This video to know all about Inverse Trigonometric Functions

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00:00 - Introduction
07:18 - Inverse Trigonometric Functions
36:12 - Basic Questions
49:17 - Domain and Range Questions
1:18:50 - Properties of ITF
3:16:42 - Transformation by Substitution
3:50:35 - Summation of Series

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[deepakkumarnayak]

00:00​ - Introduction
07:18​ - Inverse Trigonometric Functions
36:12​ - Basic Questions
49:17​ - Domain and Range Questions
1:18:50​ - Properties of ITF
3:16:42​ - Transformation by Substitution
3:50:35​ - Summation of Series

[chetanmittal]

Only one shot which is much better than full length lectures of other teachers. Thank you Sir .and plz take extra session of advanced pyqs

[tardhaiapun]

DIY ans for 1:14:09 is A and C [Max Range]
1:09:35 [JA]=concept of Comparing angles which we know with unknown
1:57:23 JM = Application Of formula!

[RahulKumar-wwlg]

properties
1:18:50
1:20:40
1:24:10
1:47:40
2:26:10
2:32:00
2:53:50

[sasankasekharsahu]

Sir this bounceback series is really amazing.... best one🔥🔥🔥🔥

[swayamdwivedi]

D.I.Y. question's answer are :-
Q.No. 1):- Option A):- 1
Option C):- 9
Q.No. 2):- Option C):- 3π/2
Q.No. 3):- Option D):- sin^(-1) {9/5√10}
Q.No. 4):- Option B):- 25/23

[mahek]

These one shots of NV sir are pure gold❤️

[INDIAN_STUDENT]

Tesla method

Tesla Method for Inverse Trigonometric Functions

The Tesla Method is a systematic approach to simplify expressions involving inverse trigonometric functions without relying on graphs or periodicity. This method ensures that the angle is always within the principal range of the inverse trigonometric function, making it easier to find the correct value.

#### Steps of the Inverse Tesla Method

1. **Remove Multiples of \(2\pi\)**:
- For any given angle \(x\), first remove the multiples of \(2\pi\) to bring it within the range \([0, 2\pi)\).
- Example: For \(15\pi\), we have \(15\pi = 2 \times 7\pi + \pi\), so we remove \(14\pi\), leaving us with \(\pi\).

2. **Consider the Range of the Inverse Trigonometric Function**:
- Identify the principal range of the inverse function.
- Example: For \(\sin^{-1}(x)\), the range is \([- \frac{\pi}{2}, \frac{\pi}{2}]\).

3. **Adjust Within the Range**:
- Subtract \(n\pi\) to bring the angle within the principal range of the inverse function.
- Example: For \(\sin^{-1}(\sin(5\pi/6))\), subtract \(\pi\): \(5\pi/6 - \pi = -\pi/6\).

4. **Determine the Sign**:
- Check the original angle's quadrant to determine the sign of the result.
- Example: Since \(5\pi/6\) is in the second quadrant where sine is positive, the result should be positive.

#### Examples

1. **Example 1: \(\sin^{-1}(\sin(5\pi/6))\)**
- **Step 1**: \(5\pi/6\) is already less than \(2\pi\).
- **Step 2**: Subtract \(\pi\): \(5\pi/6 - \pi = -\pi/6\).
- **Step 3**: Since \(5\pi/6\) is in the second quadrant where sine is positive, the result should be positive.
- **Result**: \(\sin^{-1}(\sin(5\pi/6)) = \pi/6\).

2. **Example 2: \(\cos^{-1}(\cos(9\pi/4))\)**
- **Step 1**: \(9\pi/4\) is more than \(2\pi\), so we remove \(2\pi\): \(9\pi/4 - 2\pi = \pi/4\).
- **Step 2**: The range of \(\cos^{-1}(x)\) is \([0, \pi]\). Since \(\pi/4\) is within this range, no further adjustment is needed.
- **Result**: \(\cos^{-1}(\cos(9\pi/4)) = \pi/4\).

3. **Example 3:
- **Step 1**: \(17\pi/4\) is more than \(2\pi\), so we remove \(4\pi\): \(17\pi/4 - 4\pi = \pi/4\).
- **Step 2**: The range of \(\tan^{-1}(x)\) is \((- \frac{\pi}{2}, \frac{\pi}{2})\). Since \(\pi/4\) is within this range, no further adjustment is needed.
- **Result**: \(\tan^{-1}(\tan(17\pi/4)) = \pi/4\).

4. **Example 4:
- **Step 1**: \(15\pi/2\) is more than \(2\pi\), so we remove \(7\pi\): \(15\pi/2 - 7\pi = \pi/2\).
- **Step 2**: The range of \(\cot^{-1}(x)\) is \((0, \pi)\). Since \(\pi/2\) is within this range, no further adjustment is needed.
- **Result**: \(\cot^{-1}(\cot(15\pi/2)) = \pi/2\).

### Conclusion

The Tesla Method provides a systematic and efficient way to handle inverse trigonometric functions, ensuring the angle is always within the principal range and simplifying the process without relying on graphs or periodicity.

[ayushishuklaa]

Sir apse pdhke regret horha h ki kash apke channel ko phle dhundh liya hota😭 bestest teacher!!❤️❤️❤️

[vaniamangla]

23:03 graphs
32:00 domain range
sininverse sin graphs 1:23:00

[brishti]

Mr Nishant Vora, your knowledge on the subject is impeccable !! 👍

[AnilMishra-lohs]

a lottt!!
Better one shot than 7-8 2-3 hr lecture and even then not getting the output as in your one shot!

[sarveshpandey]

2:52:58 option c coming tan-1(63/16)+cot-1(63/16) =pi/2 . Last step mai 2pi-pi/2 kiyaa

[ArunaChada-uc]

3:14:30 How cos–¹{ cos (kx+¢)} can be written as (kx+¢) without graph

[grishmitaagrawal]

NV sir has the unique and awesomeeee talent of making nihaytii bekarrr se bekaar chapter superrr NV STYLE🥳🤠

[animeblade]

I am student of first year I am only come for see NV SIR, study with NV SIR was best memories, I can't find proffesors like NV SIR

[abhaypal]

sir ye T-shirt 👕 aap ke uper bahut accha lag raha hai

[rohithsai]

4:06:42
for people who remember, it is the maximum no. of electrons which can be accommodated in 'n' th orbit

[nonidhgupta]

1:14:11 Option A and Option C are correct