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

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

Show that : cot^(-1) [(sqrt(1 + sinx) + sqrt(1 - sinx))/(sqrt(1 + sinx) - sqrt(1 - sinx))]= x/2

(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))=? (x is in IV quadrant)

Differentiate w.r.t. x the function in cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))],0ltxltpi/2

The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx))} , where (pi)/2ltxltpi , is

If y(x) = cot^(-1) ((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))), x in ((pi)/(2), pi) , then (dy)/(dx) at x=(5pi)/(6) is :

The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx) -sqrt(1+sinx))} is (0 lt x lt (pi)/(2))

Find (dy)/(dx) of y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]