" 6."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 function in Exercises 1 to 11. cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))],0 lt x lt (pi)/(2) .

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))]

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

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 function 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) [ 2 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 in(0,(pi)/(4))