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NCERT Solutions for Class 12 Math Chapter 2 – Inverse Trigonometric Functions

January 19, 2021 by SSCGuides Leave a Comment

Topics and Sub Topics in Class 11 Maths Chapter 2 Inverse Trigonometric Functions:

Section NameTopic Name
2Inverse Trigonometric Functions
2.1Introduction
2.2Basic Concepts
2.3Properties of Inverse Trigonometric Functions
  • NCERT Solutions for Class 12 (All Chapter)
  • NCERT Solutions for Class 12 Physics
  • NCERT Solutions for Class 12 Chemistry
  • NCERT Solutions for Class 12 Math
  • NCERT Solutions for Class 12 Biology
  • NCERT Solutions for Class 12 Economics
  • NCERT Solutions for Class 12 English
Contents show
1 NCERT Solutions for Class 12 Math Chapter 2
1.1 Page No 41:
1.2 Question 1:
1.3 Answer:
1.4 Question 2:
1.5 Answer:
1.6 Question 3:
1.7 Answer:
1.8 Question 4:
1.9 Answer:
1.10 Question 5:
1.11 Answer:
1.12 Question 6:
1.13 Answer:
1.14 Page No 42:
1.15 Question 7:
1.16 Answer:
1.17 Question 8:
1.18 Answer:
1.19 Question 9:
1.20 Answer:
1.21 Question 10:
1.22 Answer:
1.23 Question 11:
1.24 Answer:
1.25 Question 12:
1.26 Answer:
1.27 Question 13:
1.28 Answer:
1.29 Question 14:
1.30 Answer:
1.31 Page No 47:
1.32 Question 1:
1.33 Answer:
1.34 Question 2:
1.35 Answer:
1.36 Question 3:
1.37 Answer:
1.38 Question 4:
1.39 Answer:
1.40 Question 5:
1.41 Answer:
1.42 Question 6:
1.43 Answer:
1.44 Question 7:
1.45 Answer:
1.46 Question 8:
1.47 Answer:
1.48 Page No 48:
1.49 Question 9:
1.50 Answer:
1.51 Question 10:
1.52 Answer:
1.53 Question 11:
1.54 Answer:
1.55 Question 12:
1.56 Answer:
1.57 Question 13:
1.58 Answer:
1.59 Question 14:
1.60 Answer:
1.61 Question 15:
1.62 Answer:
1.63 Question 16:
1.64 Answer:
1.65 Question 17:
1.66 Answer:
1.67 Question 18:
1.68 Answer:
1.69 Question 19:
1.70 Answer:
1.71 Question 20:
1.72 Answer:
1.73 Question 21:
1.74 Answer:
1.75 Page No 51:
1.76 Question 1:
1.77 Answer:
1.78 Question 2:
1.79 Answer:
1.80 Question 3:
1.81 Answer:
1.82 Question 4:
1.83 Answer:
1.84 Question 5:
1.85 Answer:
1.86 Question 6:
1.87 Answer:
1.88 Question 7:
1.89 Answer:
1.90 Question 8:
1.91 Answer:
1.92 Page No 52:
1.93 Question 9:
1.94 Answer:
1.95 Question 10:
1.96 Answer:
1.97 Question 11:
1.98 Answer:
1.99 Question 12:
1.100 Answer:
1.101 Question 13:
1.102 Answer:
1.103 Question 14:
1.104 Answer:
1.105 Question 15:
1.106 Answer:
1.107 Question 16:
1.108 Answer:
1.109 Question 17:
1.110 Answer:
2 NCERT Solutions for Class 12 Maths

NCERT Solutions for Class 12 Math Chapter 2

Page No 41:

Question 1:

Find the principal value of 

Answer:

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 

Answer:

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)

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 

Question 4:

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 

Question 5:

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 

Question 6:

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 


Page No 42:

Question 7:

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 

Question 8:

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 

Question 9:

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 

Question 10:

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 

Question 11:

Find the value of 

Answer:

Question 12:

Find the value of 

Answer:

Question 13:

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,.

Question 14:

Find the value of is equal to

(A) π (B)  (C)  (D) 

Answer:


Page No 47:

Question 1:

Prove 

Answer:

To prove: 

Let x = sinθ. Then, 

We have,

R.H.S. =

= 3θ

= L.H.S.

Question 2:

Prove 

Answer:

To prove:

Let x = cosθ. Then, cos−1 x =θ.

We have,

Question 3:

Prove 

Answer:

To prove:

Question 4:

Prove 

Answer:

To prove: 

Question 5:

Write the function in the simplest form:

Answer:

Question 6:

Write the function in the simplest form:

Answer:

Put x = cosec θ ⇒ θ = cosec−1 x

Question 7:

Write the function in the simplest form:

Answer:

Question 8:

Write the function in the simplest form:

Answer:

tan-1cosx-sinxcosx+sinx=tan-11-sinxcosx1+sinxcosx=tan-11-tanx1+tanx=tan-11-tan-1tanx        tan-1x-y1+xy=tan-1x-tan-1y=π4-x


Page No 48:

Question 9:

Write the function in the simplest form:

Answer:

Question 10:

Write the function in the simplest form:

Answer:

Question 11:

Find the value of 

Answer:

Let. Then,

Question 12:

Find the value of 

Answer:

Question 13:

Find the value of 

Answer:

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.

Answer:

On squaring both sides, we get:

Hence, the value of x is

Question 15:

If, then find the value of x.

Answer:

Hence, the value of x is 

Question 16:

Find the values of 

Answer:

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 

Answer:

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 

Answer:

Let. Then,

Question 19:

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 −1x.

Here,

Now, can be written as:

cos-1cos7π6 = cos-1cosπ+π6cos-1cos7π6 = cos-1- cosπ6             as, cosπ+θ = – cos θcos-1cos7π6  = cos-1- cosπ-5π6cos-1cos7π6 = cos-1– cos 5π6   as, cosπ-θ = – cos θ

The correct answer is B.

Question 20:

Find the values of is equal to

(A)  (B)  (C)  (D) 1

Answer:

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) 

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.


Page No 51:

Question 1:

Find the value of 

Answer:

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 

Answer:

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 

Answer:

Now, we have:

Question 4:

Prove 

Answer:

Now, we have:

Question 5:

Prove 

Answer:

Now, we will prove that:

Question 6:

Prove 

Answer:

Now, we have:

Question 7:

Prove 

Answer:

Using (1) and (2), we have

Question 8:

Prove 

Answer:

Page No 52:

Question 9:

Prove 

Answer:

Question 10:

Prove 

Answer:

Question 11:

Prove  [Hint: putx = cos 2θ]

Answer:

Question 12:

Prove 

Answer:

Question 13:

Solve

Answer:

Question 14:

Solve

Answer:

Question 15:

Solveis equal to

(A)  (B)  (C)  (D) 

Answer:

Let tan−1 x = y. Then, 

The correct answer is D.

Question 16:

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.

Question 17:

Solveis equal to

(A)  (B).  (C)  (D) 

Answer:

Hence, the correct answer is C.

NCERT Solutions for Class 12 Maths

  • Chapter 1 – Relations and Functions
  • Chapter 2 – Inverse Trigonometric Functions
  • Chapter 3 – Matrices
  • Chapter 4 – Determinants
  • Chapter 5 – Continuity and Differentiability
  • Chapter 6 – Application of Derivatives
  • Chapter 7 – Integrals
  • Chapter 8 – Applications of Integrals
  • Chapter 9 – Differential Equations
  • Chapter 10 – Vector Algebra
  • Chapter 11 – Three dimensional Geometry
  • Chapter 12 – Linear Programming
  • Chapter 13 – Probability
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