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:
Solve
is 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:



Thus, x = 0.
Hence, the correct answer is C.
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Question 17:
Solve
is equal to

(A)
(B).
(C)
(D) 




ANSWER:

Hence, the correct answer is C.