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NCERT solution class 12 chapter 2 Inverse Trigonometric Functions exercise 2.1 mathematics part 1

EXERCISE 2.1


Page No 41:

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 

Page No 42:

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 y, then

(A)  (B) 

(C)  (D) 

Answer:

It is given that sin−1 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:


 

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