tan^(-1)(1+sin x)/(cos^(2)x)

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

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

The value of tan(sin^(-1)(cos(sin^(-1)x)))tan(cos^(-1)(sin(cos^(-1)x)))." where "x in (0, 1) is equal to

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

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

If sin^(-1)x in (0, (pi)/(2)) , then the value of tan((cos^(-1)(sin(cos^(-1)x))+sin^(-1)(cos(sin^(-1)x)))/(2)) is :

If sin^(-1)x in (0, (pi)/(2)) , then the value of tan((cos^(-1)(sin(cos^(-1)x))+sin^(-1)(cos(sin^(-1)x)))/(2)) is :

The value of tan(sin^(-1)(cos(sin^(-1)x)))tan(cos^(-1)(sin(cos^(-1)x))), where x in(0,1) is equal to 0(b)1(c)-1(d) none of these

The value of tan {sin^(-1)(cos(sin^(-1)x))} tan{cos^(-1) (sin(cos^(-1)x))} x in (0,1) a)0 b)1 c)-1 d)None of these