Prove that:`cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2, x in (0,pi/4)`

Prove That : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x epsilon(0,(pi)/4)

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

Prove the following : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2^,x in (0,pi/4)

Tan^(-1)[(sqrt(1+sinx)-sqrt(1-sinx))/(sqrt(1+sinx)+sqrt(1-sinx))]=

Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/(2), 0 lt x lt (pi)/(2), or x in (0, (pi)/(4)) .

Prove that: cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}=pi/2-x/2 , if pi/2 < x < pi

Prove the following: cot^(-1)[(sqrt(1+sinx )+sqrt(1-sinx))/(sqrt(1+sinx)-\ sqrt(1-sinx))]=x/2,\ x (0,pi/4)

y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),find dy/dx.

cot^(-1)((sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx)))=...(0ltxltpi/2)