Question

If |x| ≤ 1, then 2tan^-1 x – sin^-1 2x/(1 + x²) is equal to …..

(a) tan^-1 x 

(b) sin^-1 x 

(c) 0 

(d) π

Answer 1

(c) 0

Let x = tan θ so 2x/(1 + x²) = sin 2θ.

Now 2 tan^-1(tanθ) – sin^-1(sin 2θ) = 2θ – 2θ = 0