# Miscellaneous Exercise - Chapter 2 Inverse Trigonometry class 12 ncert solutions Maths - SaraNextGen [2024]

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:

Solveis equal to

(A)  (B)  (C)  (D)

Let tan−1 x = y. Then,

Question 16:

Solvethen 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:

Solveis equal to

(A)  (B).  (C)  (D)