Updated By SaraNextGen

On March 11, 2024, 11:35 AM

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:

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:

Question 3:

Prove 

Answer:

Now, we have:

Question 4:

Prove 

Answer:

Now, we have:

Question 5:

Prove 

Answer:

Now, we will prove that:

Question 6:

Prove 

Answer:

Now, we have:

Question 7:

Prove 

Answer:

Using (1) and (2), we have

Question 8:

Prove 

Answer:

Question 9:

Prove 

Answer:

Question 10:

Prove 

Answer:

Question 11:

Prove  [Hint: putx = cos 2θ]

Answer:

Question 12:

Prove 

Answer:

Question 13:

Solve

Answer:

Question 14:

Solve

Answer:

Question 15:

Solveis equal to

(A)  (B)  (C)  (D) 

Answer:

Let tan⁻¹ x = y. Then, 

The correct Answer is D.

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.

Question 17:

Solveis equal to

(A)  (B).  (C)  (D) 

Answer:

Hence, the correct Answer is C.