Here is a NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions. This solutions covers all questions of Maths Chapter 2 Inverse Trigonometric Functions Class 12 as per CBSE Board guidelines from the latest NCERT book for class 12 maths. Following topics and sub-topics in Class 12 Maths Chapter 2 Inverse Trigonometric Functions are covered.

2.1 Introduction

2.2 Basic Concepts

2.3 Properties of Inverse Trigonometric Functions.

## Inverse Trigonometric Functions NCERT Solutions – Class 12 Maths

### NCERT Solutions for Class 12 Maths Chapter 2

**Q1 : Find the principal value of **

**Answer :**

Let =y. Then sin y=

We know that the range of the principal value branch of sin^{-1} is

and sin

Therefore, the principal value of

**Q2 :**

**Find the principal value of**

**Answer :**

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

^{-1}is

Therefore, the principal value of.

**Q3 :**

**Find the principal value of cosec**

^{-1}(2)**Answer :**

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

**Q4 :**

**Find the principal value of**

**Answer :**

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

^{ -1}is

Therefore, the principal value of

**Q5 :**

**Find the principal value of**

**Answer :**

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

^{ -1}is

Therefore, the principal value of

**Q6 : Find the principal value of tan**

^{-1}(-1)**Answer :**

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

**Q7 : Find the principal value of**

**Answer :**

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

^{-1}is

Therefore, the principal value of

**Q8 :Find the principal value of**

**Answer :**

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

^{-1}is

(0,π) and

Therefore, the principal value of

**Q9 : Find the principal value of**

**Answer :**

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

^{-1}is [0,π] and

Therefore, the principal value of

**Q10 : Find the principal value of**

**Answer :**

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

^{-1}is

Therefore, the principal value of

**Q11 :**

**Find the value of**

**Answer :**

**Q12 :Find the value ofAnswer :**

**Q13 :Find the value of if sin – 1 x = y, then**

**(A) (B)**

**(C) (D)**

**Answer :**

It is given that sin

^{-1}x = y.

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

^{-1}is

Therefore,.

**Q14 :Find the value of is equal to**

**(A) π (B) (C) (D)**

**Answer**

**Exercise 2.2 : Solutions of Questions on Page Number : 47**

**Q1 :Prove**

**Answer :**

To prove:

Let x = sinθ. Then,

We have,

R.H.S. =

= 3θ

= L.H.S.

**Q2 :Prove**

**Answer :**

To prove:

Let x = cosθ. Then, cos

^{-1}x =θ.

We have,

**Q3 :Prove**

**Answer :**

To prove:

**Q4 :Prove**

**Answer :**

To prove:

**Q6 :Write the function in the simplest form:**

**Answer :**

Put x = cosec θ ⇒ θ = cosec

^{-1}x

**Q7 :Write the function in the simplest form:**

**Answer :**

**Q8 :Write the function in the simplest form:**

**Answer :**

**Q9 :Write the function in the simplest form:**

**Answer :**

**Q10 :Write the function in the simplest form:**

**Answer :**

**Q11 :Find the value of**

**Answer :**

Let. Then,

**Q12 :Find the value of**

**Answer :**

**Q13 :Find the value of**

**Answer :**

Let x = tan θ. Then, θ = tan

^{-1}x.

Let y = tan Φ. Then, Φ = tan

^{-1}y.

**Q14 :If, then find the value of x.**

**Answer :**

On squaring both sides, we get:

Hence, the value of x is

**Q15 :If, then find the value of x.**

**Answer :**

Hence, the value of x is

**Q16 :Find the values of**

**Answer :**

We know that sin

^{-1}(sin x) = x if, which is the principal value branch of sin

^{-1}x.

Here,

Now, can be written as:

**Q17 :Find the values of**

**Answer :**

We know that tan

^{-1}(tan x) = x if, which is the principal value branch of tan

^{-1}x.

Here,

Now, can be written as:

**Q18 :**

**Find the values of**

**Answer :**

Let. Then,

**Q19 :Find the values of is equal to**

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

**Answer :**

We know that cos

^{-1}(cos x) = x if, which is the principal value branch of cos

^{-1}x.

Here,

Now, can be written as:

The correct answer is B.

**Q20 :Find the values of is equal to**

**Answer :**

Let . Then

We know that the range of the principle value branch of

The correct answer is D.

**Q21 :Find the values of is equal to**

**(A) π (B) (C) 0 (D)**

**Answer :**

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.

**Exercise Miscellaneous : Solutions of Questions on Page Number : 51**

**Q1 :Find the value of**

**Answer :**

We know that cos

^{-1}(cos x) = x if, which is the principal value branch of cos

^{-1}x.

Here,

Now, can be written as:

**Q2 :**

**Find the value of**

**Answer :**

We know that tan

^{-1}(tan x) = x if, which is the principal value branch of tan

^{-1}x.

Here,

Now, can be written as:

**Q3 :Prove**

**Answer :**

Now, we have:

**Q4 :Prove**

**Answer :**

Now, we have:

**Q5 :Prove**

**Answer :**

Now, we will prove that:

**Q6 :Prove**

**Answer :**

Now, we have:

**Q7 :Prove**

**Answer :**

Using (1) and (2), we have

**Q8 :Prove**

**Answer :**

**Q9 :Prove**

**Answer :**

**Q10 :Prove**

**Answer :**

**Q11 :Prove [Hint: putx = cos 2θ]**

**Answer :**

**Q12 :Prove**

**Answer :**

**Q13 :Solve**

**Answer :**

**Q14: Solve**

**Answer:**

**Q15 :Solveis equal to**

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

**Answer :**

Let tan – 1 x = y. Then,

The correct answer is D.

**Q16 :Solve, then x is equal to**

**(A) (B) (C) 0 (D)**

**Answer :**

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.

**Q17 :Solve is equal to**

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

**Answer :**

Hence, the correct answer is C.