NCERT Solutions for Class 12 Humanities Maths Chapter 2 Inverse Trigonometric Functions are provided here with simple step-by-step explanations. These solutions for Inverse Trigonometric Functions are extremely popular among Class 12 Humanities students for Maths Inverse Trigonometric Functions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of Class 12 Humanities Maths Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s NCERT Solutions. All NCERT Solutions for class Class 12 Humanities Maths are prepared by experts and are 100% accurate.

#### Question 1:

Find the principal value of

Let sin-1 Then sin y =

We know that the range of the principal value branch of sin−1 is

and sin

Therefore, the principal value of

#### Question 2:

Find the principal value of

We know that the range of the principal value branch of cos−1 is

.

Therefore, the principal value of.

#### Question 3:

Find the principal value of cosec−1 (2)

Let cosec−1 (2) = y. Then,

We know that the range of the principal value branch of cosec−1 is

Therefore, the principal value of

#### Question 4:

Find the principal value of

We know that the range of the principal value branch of tan−1 is

Therefore, the principal value of

#### Question 5:

Find the principal value of

We know that the range of the principal value branch of cos−1 is

Therefore, the principal value of

#### Question 6:

Find the principal value of tan−1 (−1)

Let tan−1 (−1) = y. Then,

We know that the range of the principal value branch of tan−1 is

Therefore, the principal value of

#### Question 7:

Find the principal value of

We know that the range of the principal value branch of sec−1 is

Therefore, the principal value of

#### Question 8:

Find the principal value of

We know that the range of the principal value branch of cot−1 is (0,π) and

Therefore, the principal value of

#### Question 9:

Find the principal value of

We know that the range of the principal value branch of cos−1 is [0,π] and

.

Therefore, the principal value of

#### Question 10:

Find the principal value of

We know that the range of the principal value branch of cosec−1 is

Therefore, the principal value of

#### Question 11:

Find the value of

#### Question 12:

Find the value of

#### Question 13:

Find the value of if sin−1 x = y, then

(A) (B)

(C) (D)

It is given that sin−1 x = y.

We know that the range of the principal value branch of sin−1 is

Therefore,.

#### Question 14:

Find the value of is equal to

(A) π (B) (C) (D)

#### Question 1:

Prove

To prove:

Let x = sinθ. Then,

We have,

R.H.S. =

= 3θ

= L.H.S.

#### Question 2:

Prove

To prove:

Let x = cosθ. Then, cos−1 x =θ.

We have,

Prove

To prove:

Prove

To prove:

#### Question 5:

Write the function in the simplest form:

#### Question 6:

Write the function in the simplest form:

Put x = cosec θθ = cosec−1 x

#### Question 7:

Write the function in the simplest form:

#### Question 8:

Write the function in the simplest form:

#### Question 9:

Write the function in the simplest form:

#### Question 10:

Write the function in the simplest form:

#### Question 11:

Find the value of

Let. Then,

#### Question 12:

Find the value of

#### Question 13:

Find the value of

Let x = tan θ. Then, θ = tan−1 x.

Let y = tan Φ. Then, Φ = tan−1 y.

#### Question 14:

If, then find the value of x.

On squaring both sides, we get:

Hence, the value of x is

#### Question 15:

If, then find the value of x.

Hence, the value of x is

#### Question 16:

Find the values of

We know that sin−1 (sin x) = x if, which is the principal value branch of sin−1x.

Here,

Now, can be written as:

#### Question 17:

Find the values 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 18:

Find the values of

Let. Then,

#### Question 19:

Find the values of is equal to

(A) (B) (C) (D)

We know that cos−1 (cos x) = x if, which is the principal value branch of cos −1x.

Here,

Now, can be written as:

The correct answer is B.

#### Question 20:

Find the values of is equal to

(A) (B) (C) (D) 1

Let. Then,

We know that the range of the principal value branch of.

The correct answer is D.

#### Question 21:

Find the values of is equal to

(A) π (B) (C) 0 (D)

Let. Then,

We know that the range of the principal value branch of

Let.

The range of the principal value branch of

The correct answer is B.

#### 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:

Prove

Now, we have:

Prove

Now, we have:

#### Question 5:

Prove

Now, we will prove that:

Prove

Now, we have:

#### Question 7:

Prove

Using (1) and (2), we have

Prove

Prove

Prove

#### Question 11:

Prove [Hint: putx = cos 2θ]

Prove

Solve

Solve

#### Question 15:

Solveis equal to

(A) (B) (C) (D)

Let tan−1 x = y. Then,

The correct answer is D.

#### 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.

Solveis equal to

(A) (B). (C) (D)
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