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

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: 

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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: 

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Question 3:

Prove 

ANSWER:

Now, we have:

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Question 4:

Prove 

ANSWER:

Now, we have:

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Question 5:

Prove 

ANSWER:

Now, we will prove that:

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Question 6:

Prove 

ANSWER:

Now, we have:

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Question 7:

Prove 

ANSWER:

Using (1) and (2), we have

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Question 8:

Prove 

ANSWER:

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Question 9:

Prove 

ANSWER:

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Question 10:

Prove 

ANSWER:

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Question 11:

Prove  [Hint: putx = cos 2θ]

ANSWER:

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Question 12:

Prove 

ANSWER:

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Question 13:

Solve

ANSWER:

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Question 14:

Solve

ANSWER:

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Question 15:

Solveis equal to

(A) (B)  (C) (D)  

ANSWER:

Let tan−1 x = y. Then, 

The correct answer is D.

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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.

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Question 17:

Solveis equal to

(A)  (B).  (C)  (D) 

ANSWER:

Hence, the correct answer is C.