Class 12 NCERT Solutions- Mathematics Part I – Chapter 2 Inverse Trigonometric Functions – Miscellaneous Exercise on Chapter 2 | Set 2

Chapter 2 Inverse Trigonometric Functions – Miscellaneous Exercise on Chapter 2 | Set 1 

Question 11. Prove 

Solution:

Put so that, 

Then, we have :

LHS = 

= 

= 

= 

= 

      – 

L.H.S = R.H.S

Hence Proved

Question 12. Prove 

Solution:

L.H.S. = 

= 

Using 

=       -(1)

Now, let  Then, 

Using equation(1), we get,

= 

L.H.S = R.H.S

Hence Proved

Question 13. Solve 

Solution:

=                      –

= 

= 

= cos x/sin x

= cot x =1

Therefore, x = π/4​

Question 14. Solve 

Solution:

Let x = tanθ

π/4 – θ = θ/2

θ = π/6

So, x = tan(π/6) = 1/√3

Question 15. Solve  is equal to

(A)     (B)  (C) (D) 

Solution:

Let tan y = x, 

Let  Then,

So, the correct answer is D.

Question 16. Solve , then x is equal to

(A) 0, 1/2      (B) 1, 1/2      (C) 0     (D) 1/2 

Solution:

        -(1)

Let 

Therefore, from equation(1), we have

Put x = siny then, we have:

sin y = 0 or 1/2

x = 0 or x = 1/2

But, when x = 1/2 it can be observed that:

L.H.S. = 

= 

= 

= 

x = 1/2 is not the solution of given equation.

Thus, x = 0 

Hence, the correct answer is C

Question 17. Solve  is equal to

(A) π​/2      (B) π​/3     (C) π​/4      (D) -3π​/4  

Solution

                –

Hence, the correct answer is C