Class 12-commerce NCERT Solutions Maths Chapter 2 - Inverse Trigonometric Functions
Ex. 2.1
Ex. 2.2
Misc. Ex.
Inverse Trigonometric Functions Exercise Ex. 2.1
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/2169_soluq2_1.gif)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/2170_soluq2_2.gif)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/2171_soluq2_3.gif)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/2172_soluq2_4.gif)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/2173_soluq2_5.gif)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/2174_soluq2_6.gif)
Solution 7
We know that the range of the principal value of sec-1 is
Solution 8
Solution 9
![](https://images.topperlearning.com/topper/bookquestions/2177_soluq2_9.gif)
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/2178_soluq2_10.gif)
Solution 11
![](https://images.topperlearning.com/topper/bookquestions/2179_soluq2_11.gif)
Solution 12
![](https://images.topperlearning.com/topper/bookquestions/2180_soluq2_12.gif)
Solution 13
![](https://images.topperlearning.com/topper/bookquestions/2181_soluq2_13.gif)
Solution 14
Inverse Trigonometric Functions Exercise Ex. 2.2
Solution 1
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/2382_soluq2_16.gif)
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Inverse Trigonometric Functions Exercise Misc. Ex.
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/2466_solumis_1.gif)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/2467_solumis_2.gif)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/2468_solumis_3.gif)
Solution 4
Solution 5
= by (3)
= RHS
Solution 6
Let sin-1(3/5) = A and cos-1 (12/13) = B
So sin A = 3/5 and cos B = 12/13
Hence cos A = 4/5 and sin B = 5/13
As R.H.S is sin-1 we use sin (A + B)
Sin (A + B) = sin A cos B + cos A sin B = (3/5) (12/13) + (4/5) (5/13)
= 36/65 + 20/65 = 56/65
Thus A + B = sin-1 (56/65) hence proved.
Concept insight:
If R.H.S is cos-1 or sin-1 then use Cos (A + B) or sin (A + B) as the case may be.
Solution 7
Solution 8