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))}=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)

Differentiate w.r.t. x the function cot^(-1)""((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),0 < x < pi/2

int(sinx)/(sqrt(1+sinx))dx

Differentiate tan^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))} , 0 < x < pi

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

The value of tan^(-1)[(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx))](AA x in [0, (pi)/(2)]) is equal to

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=

" If "y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))](0ltxltpi//2)," then "(dy)/(dx)=