What is  equal to?

Concept:

• Sin2 θ + cos2 θ = 1
• 1 + tan2 θ = sec2 θ
• 1 +cot2 θ = cosec2 θ
• 2 sin θ cos θ = sin 2θ  
• sin-1 sin x = x

Calculation:

We have to find the value of 

Let y =  

put x = tan θ

= sin-1 (2 × sin θ × cos θ)

= sin-1 (sin 2θ)     (sin 2θ = 2 sin θ cos θ)

= 2θ               (∵ sin-1 sin x = x)

= 2 tan-1 x      (∵ x = tan θ)

So, y = 2 tan-1 x

Differentiating with respect to x, we get

∴ Option 3 is correct.