### Miscellaneous Exercise No. 2 Chapter 2 - Inverse Trigonometric Functions NCERT Solutions for Class 12 Science Math

#### Question 1:

Find the value of We know that cos−1 (cos x) = x if , which is the principal value branch of cos −1x.
Here, Now, can be written as: #### Question 2:

Find the value of We know that tan−1 (tan x) = x if , which is the principal value branch of tan −1x.
Here, Now, can be written as:  #### Question 3:

Prove  Now, we have: #### Question 4:

Prove  Now, we have: #### Question 5:

Prove  Now, we will prove that: #### Question 6:

Prove  Now, we have: #### Question 7:

Prove  Using (1) and (2), we have #### Question 8:

Prove  #### Question 9:

Prove  #### Question 10:

Prove  #### Question 11:

Prove [Hint: putx = cos 2θ] #### Question 12:

Prove  #### Question 13:

Solve   #### Question 14:

Solve  #### Question 15:

Solve is equal to
(A) (B) (C) (D) Let tan−1 x = y. Then,  #### Question 16:

Solve then x is equal to
(A) (B) (C) 0 (D)  Therefore, from equation (1), we have Put x = sin y. Then, we have: But, when , it can be observed that:  is not the solution of the given equation.
Thus, x = 0.
Hence, the correct answer is C.

#### Question 17:

Solve is equal to
(A) (B). (C) (D)  