Differentiate the following w.r.t. x : sin^2 [cot^-1 (√(1 + x)/(1 - x))]

Question

Differentiate the following w.r.t. x :

\(sin^2 \left[cot^{-1} \left(\sqrt{\frac{1 + x}{1 - x}}\right)\right]\)

sin² [cot^-1 (√(1 + x)/(1 - x))]

Answer 1

sin² [cot^-1 (√(1 + x)/(1 - x))]

\(sin^2 \left[cot^{-1} \left(\sqrt{\frac{1 + x}{1 - x}}\right)\right]\)

Put x = cos θ. Then θ = cos^-1 x and