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


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:

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.

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