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

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

### (A)     (B)  (C) (D)

Solution:

Let tan y = x,

Let  Then,

So, the correct answer is D.

### (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

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

Solution

–

Hence, the correct answer is C

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