" 4."tan^(-1)((sin x)/(1+cos x))

tan^(-1)((cos x)/(1+sin x))

tan^(-1)((cos x)/(1-sin x))

Prove that , tan^(-1)((2 sin 2x)/(1+2 cos 2x))-(1)/(2)sin^(-1)((3 sin 2x)/(5+4 cos 2x))=x .

tan^(-1)((1-cos x)/(sin x))

The derivative of tan^(-1)[(sin x)/(1+cos x)] w.r.t tan^(-1) [(cos x)/( 1+ sin x)] is

Find the derivative with tan^(-1) ((sinx )/(1 + cos x)) with respect to tan^(-1) ((cos x)/(1 + sin x))

Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^(-1)(sin x/(1+cos x)) (iii) sin ^(-1)((2^(x+1))/(1+4^x))

Prove that, tan^(-1)((3 sin 2x)/(5+3 cos 2x))+tan^(-1)((1)/(4) tan x)=x .