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 -1is

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-1is
Therefore, the principal value of


Q4 : Find the principal value of
Answer :
We know that the range of the principal value branch of tan -1is

Therefore, the principal value of


Q5 : Find the principal value of
Answer :
We know that the range of the principal value branch of cos -1is

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-1x.
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.