Chapter 2 - Inverse Trigonometric Functions
NCERT Solutions for Class 12 Science Math
Exercise No. 2.2
Question 1:
Prove 

ANSWER:
To prove: 

Let x = sinθ. Then, 

We have,
R.H.S. =


= 3θ

= L.H.S.
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Question 2:
Prove 

ANSWER:
To prove:

Let x = cosθ. Then, cos−1 x =θ.
We have,

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Question 3:
Prove 

ANSWER:
To prove:


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Question 4:
Prove 

ANSWER:
To prove: 


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Question 5:
Write the function in the simplest form:

ANSWER:

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Question 6:
Write the function in the simplest form:

ANSWER:

Put x = cosec θ ⇒ θ = cosec−1 x

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Question 7:
Write the function in the simplest form:

ANSWER:

Question 8:
Write the function in the simplest form:
Write the function in the simplest form:

ANSWER:
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Question 9:
Write the function in the simplest form:

ANSWER:

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Question 10:
Write the function in the simplest form:

ANSWER:

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Question 11:
Find the value of 

ANSWER:
Let
. Then,



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Question 12:
Find the value of 

ANSWER:

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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.

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Question 14:
If
, then find the value of x.

ANSWER:

On squaring both sides, we get:


Hence, the value of x is

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Question 15:
If
, then find the value of x.

ANSWER:

Hence, the value of x is 

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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:



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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:



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Question 18:
Find the values of 

ANSWER:
Let
. Then,



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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.
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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.