Exercise 2.1

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NCERT Solutions class 12 Maths Inverse Trigonometric Function

Find the principal values of the following:

1.  

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of  is

2.

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

3.  

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

4.

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

5.

Ans. Let

Since, the principal value branch of  is

Therefore,  Principal value of   is

6.  

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

7.

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

8.

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

9.  

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

10.

Ans. Let

Since, the principal value branch of  is

Therefore, Principal value of   is

Find the value of the following:

11.

Ans.

=

=

=

=  =

12.  

Ans.

=

=

=

NCERT Solutions class 12 Maths Exercise 2.1

13. If   then:

A)

(B)

(C)  

(D)

Ans. By definition of principal value for  

Therefore, option (B) is correct.

14.   is equal to:

(A)

(B)

(C)

(D)  

Ans.

=

=

=

Therefore, option (B) is correct.