(d)/(dx)[cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))]" equals: "

(d)/(dx) [ 2 cot^(-1) ((sqrt(1+ sin x) + 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)

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

Differentiate w.r.t x the function 0 lt x lt (pi)/(2), cot^(-1) [(sqrt(1 + sin x) + sqrt(1-sin x))/(sqrt(1+ sin x)-sqrt(1-sin x))]

Prove that 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))

Prove that 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))

the expression ((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=

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))]