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NCERT Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions


Free NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions solved by Expert Teachers as per NCERT (CBSE) Book guidelines and brought to you by Toppers Bulletin. These Inverse Trigonometric Functions Exercise Questions with Solutions for Class 12 Maths covers all questions of Chapter Inverse Trigonometric Functions Class 12 and help you to revise complete Syllabus and Score More marks as per CBSE Board guidelines from the latest NCERT book for class 12 maths. You can read and download NCERT Book Solution to get a better understanding of all topics and concepts
2.1 Introduction
2.2 Basic Concepts
2.3 Properties of Inverse Trigonometric Functions.

Inverse Trigonometric Functions NCERT Solutions – Class 12 Maths

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.

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