NCERT Solutions class 12 Maths Exercise Miscellaneous Ch 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Exercise 2.1 Chapter 2 Inverse Trigonometric Functions – FREE PDF Download

NCERT Class 12 Maths Ch 2 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 12 Maths Chapter 2 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 12 inverse trigonometry solutions will help you understand the chapter thoroughly.

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

Find the value of the following:

1.

Ans.

=

=

=

= =

2.

Ans.

=

=

=

= =

3. Prove that:

Ans. Let

so that

Since

= = =

4. Prove that:

Ans. Let

so that

Again, Let so that

Since

=

=

5. Prove that:

Ans. Let

so that

Again, Let so that

Since =

=

6. Prove that:

Ans. Let

so that

Again, Let so that

Since = $\frac{5}{13} \times \frac{4}{5} + \frac{12}{13} \times \frac{3}{5}$

=

7. Prove that:

Ans. Let

so that

Again, Let so that

Since =

=

8. Prove that:

Ans. L.H.S. =

=

=

=

=

=

=

R.H.S.

9. Prove that:

Ans. Let

so that

=

=

=

=

10. Prove that:

Ans. We know that

=

Again,

=

L.H.S. =

=

=

=

11. Prove that:

Ans. Putting

so that

L.H.S. =

=

=

=

Dividing every term by

=

=

= =

= = R.H.S.

12. Prove that:

Ans. L.H.S. =

=

= …(i)

Now, let so that

$\Rightarrow$ $θ = \sin^{- 1} \frac{2 \sqrt{2}}{3}$

From eq. (i), = R.H.S.

13. Solve the equation:

Ans.

14. Solve the equation:

Ans. Putting

15. is equal to:

(A)

(B)

(C)

(D)

Ans. Let

where

so that

Putting

Therefore, option (D) is correct.

16. then is equal to:

(A)

(B)

(C) 0

(D)

Ans. Putting

so that

or

or

But does not satisfy the given equation.

Therefore, option (C) is correct.

17. is equal to:

(A)

(B)

(C)

(D)

Ans.

=

=

=

=

=

=

Therefore, option (C) is correct.