NCERT Solutions for Maths Class 12 Exercise 2.2

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 2.2. 

You can download the PDF of NCERT Books Maths Chapter 2 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 2.2.

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NCERT Solutions for Maths Class 12 Exercise 2.1

NCERT Solutions for Maths Class 12 Exercise 2.2

Maths Class 12 Ex 2.2 Question 1.

Prove the following.

Solution:
Let sin^-1 x = θ
sin θ = x

R.H.S. = sin^-1 (3x – 4x³)
          = sin^-1 (3 sin θ – 4 sin³ θ)
          = sin^-1 (sin 3θ)                                        [Since, sin 3θ = 3 sin θ – 4 sin³ θ]
          = 3θ
          = 3 sin^-1 x
          = L.H.S.

Maths Class 12 Ex 2.2 Question 2.

Prove the following.

Solution:

Let cos^-1 x = θ
x = cos θ
R.H.S. = cos^-1 (4x³ – 3x)
          = cos^-1 (4 cos³θ – 3 cos θ)
          = cos^-1 (cos 3θ)                                        [∴ cos 3θ = 4 cos³ θ – 3 cos θ]
          = 3θ
          = 3 cos^-1 x
          = L.H.S.

Maths Class 12 Ex 2.2 Question 3.

Write the following function in the simplest form.

Solution:
Putting x = tan θ, we get θ = tan^-1 x.

Maths Class 12 Ex 2.2 Question 4.

Write the following function in the simplest form.

Solution:

Maths Class 12 Ex 2.2 Question 5.

Write the following function in the simplest form.

Solution:

Dividing both numerator and denominator by cos x, we get

Maths Class 12 Ex 2.2 Question 6.

Write the following function in the simplest form.

Solution:
Putting x = a sin θ, we get x/a = sin θ.

Maths Class 12 Ex 2.2 Question 7.

Write the following function in the simplest form.
, a > 0; –a/√3 < x < a/√3

Solution:
Putting x = a tan θ, we get

Maths Class 12 Ex 2.2 Question 8.

Find the value of the following.

Solution:

Maths Class 12 Ex 2.2 Question 9.

Find the value of the following.

Solution:
Putting x = tan θ, we get tan^-1 x = θ.

Maths Class 12 Ex 2.2 Question 10.

Find the value of the following expression.

Solution:

Maths Class 12 Ex 2.2 Question 11.

Find the value of the following expression.

Solution:

Maths Class 12 Ex 2.2 Question 12.

Find the value of the following expression.

Solution:

Let sin^-1 3/5 = θ, then sin θ = 3/5.

Maths Class 12 Ex 2.2 Question 13.

is equal to
(A) 7π/6  
(B) 5π/6 
(C) π/3 
(D) π/6 

Solution:

Maths Class 12 Ex 2.2 Question 14.

is equal to
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1

Solution:

Hence, option (d) is correct.

Maths Class 12 Ex 2.2 Question 15.

is equal to
(A) π
(B) –π/2

(C) 0
(D) 2√3

Solution:

Related Link:

NCERT Solutions for Maths Class 12 Exercise 2.1