NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions Ex 2.1

NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions Ex 2.1

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Question 1:

Find the principal value of 

Answer:

Let sin^-1  Then sin y = 

We know that the range of the principal value branch of sin⁻¹ is

 and sin

Therefore, the principal value of 

Question 2:

Find the principal value of 

Answer:

We know that the range of the principal value branch of cos⁻¹ is

.

Therefore, the principal value of.

Question 3:

Find the principal value of cosec⁻¹ (2)

Answer:

Let cosec⁻¹ (2) = y. Then, 

We know that the range of the principal value branch of cosec⁻¹ is 

Therefore, the principal value of 

Question 4:

Find the principal value of 

Answer:

We know that the range of the principal value branch of tan⁻¹ is 

Therefore, the principal value of 

Question 5:

Find the principal value of 

Answer:

We know that the range of the principal value branch of cos⁻¹ is

Therefore, the principal value of 

Question 6:

Find the principal value of tan⁻¹ (−1)

Answer:

Let tan⁻¹ (−1) = y. Then, 

We know that the range of the principal value branch of tan⁻¹ is

Therefore, the principal value of 

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Question 7:

Find the principal value of 

Answer:

We know that the range of the principal value branch of sec⁻¹ is

Therefore, the principal value of 

Question 8:

Find the principal value of 

Answer:

We know that the range of the principal value branch of cot⁻¹ is (0,π) and

Therefore, the principal value of 

Question 9:

Find the principal value of 

Answer:

We know that the range of the principal value branch of cos⁻¹ is [0,π] and

.

Therefore, the principal value of 

Question 10:

Find the principal value of 

Answer:

We know that the range of the principal value branch of cosec⁻¹ is 

Therefore, the principal value of 

Question 11:

Find the value of 

Answer:

Question 12:

Find the value of 

Answer:

Question 13:

Find the value of if sin⁻¹ x = y, then

(A)  (B) 

(C)  (D) 

Answer:

It is given that sin⁻¹ x = y.

We know that the range of the principal value branch of sin⁻¹ is 

Therefore,.

Question 14:

Find the value of is equal to

(A) π (B)  (C)  (D) 

Answer: