tan^(-1)[[sqrt(1+sin x)+sqrt(1-sin x)],[sqrt(1+sin x)-sqrt(1-sin x)]]

If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x)]] where 0 lt x lt pi/2 find (dy)/(dx)

cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]=

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

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

If y=cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))](0

Differentiate w.r.t x the functions cot ^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]

(d)/(dx) Tan^(-1)[(sqrt(1+sinx) - sqrt(1-sin x))/(sqrt(1+sin x) + sqrt(1-sin x))]=

cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2)

(cot^(-1){sqrt(1+sin x)+sqrt(1-sin x)})/(sqrt(1+sin x)-sqrt(1-sin x))

Find the value of cot^(-1)[(sqrt(1-sin x)+sqrt(1+sin x))/(sqrt(1-sin x)-sqrt(1+sin x))]