# NCERT Solutions for Class 12 Maths Maths Part-1 Chapter 2

## Inverse Trigonometric Functions Class 12

### Exercise 2.1 : Solutions of Questions on Page Number : 41

Q1 :

Find the principal value of

Let sin-1 Then sin y=

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

and sin

Therefore, the principal value of

Q2 :

Find the principal value of

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

.

Therefore, the principal value of.

Q3 :

Find the principal value of cosec-1(2)

Q4 :

Find the principal value of

Q5 :

Find the principal value of

Q6 :

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

Q7 :

Find the principal value of

Q8 :

Find the principal value of

Q9 :

Find the principal value of

Q10 :

Find the principal value of

Q11 :

Find the value of

Q12 :

Find the valueof

Q13 :

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

(A) (B)

(C) (D)

Q14 :

Find the value of is equal to

(A) π (B) (C) (D)

### Exercise 2.2 : Solutions of Questions on Page Number : 47

Q1 :

Prove

Q2 :

Prove

Q3 :

Prove

Q4 :

Prove

Q5 :

Write the function in the simplest form:

Q6 :

Write the function in the simplest form:

Q7 :

Write the function in the simplest form:

Q8 :

Write the function in the simplest form:

Q9 :

Write the function in the simplest form:

Q10 :

Find the value of

Q11 :

Find the value of

Q12 :

Find the value of

Q13 :

If, then find the value of x.

Q14 :

If, then find the value of x.

Q15 :

Find the values of

Q16 :

Find the values of

Q17 :

Find the values of

Q18 :

Find the values of is equal to

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

Q19 :

Find the values of is equal to

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

Q20 :

Find the values of is equal to

(A) π (B) (C) 0 (D)

### Exercise Miscellaneous : Solutions of Questions on Page Number : 51

Q1 :

Find the value of

Q2 :

Find the value of

Q3 :

Prove

Q4 :

Prove

Q5 :

Prove

Q6 :

Prove

Q7 :

Prove

Q8 :

Prove

Q9 :

Prove

Q10 :

Prove

Q11 :

Prove [Hint: putx = cos 2θ]

Q12 :

Prove

Q13 :

Solve

Q14 :

Solve

Q15 :

Solve

Q16 :

Solveis equal to

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

Q17 :

Solve, then x is equal to

(A) (B) (C) 0 (D)

Q18 :

Solveis equal to

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