Simplify `sincot^(-1)tancos^(-1)x , x >0`

Simplify sin(cot^(-1)(cos(tan^(-1)x))),0 ltxlt1 .

Simplify cos(tan^(-1)(sin(cot^(-1)x))), x in (0,1) .

Simplify cot^(-1)((1)/(sqrt(x^(2)-1))), x lt -1

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

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) sincot^-1 tancos^-1 (sin gamma) is equal to (A) 2singamma (B) sin(gamma/2) (C) 1/2 sin gamma (D) cosgamma

Simplify tan^(-1)[(a cos x-b sin x)/(b cos x+a sin x)], if (a)/(b)tan x>-1

Simplify tan^(-1)((sqrt(1+x^2)-1)/x)

Simplify tan^(-1)((sinx)/(1+cos x))

Simplify :sin[2tan^(-1)sqrt((1-x)/(1+x))]