### 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 = tan

θ

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) -3*π*/4

**Solution**

–

Hence, the correct answer is C

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