" (iv) "tan^(-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))]=

(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)))]=

int_(0)^(pi//2)tan^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]\ dx

If x in(pi,(3 pi)/(2)) then the value of tan^(-1)((sqrt(1-sin x)+sqrt(1+sin x))/(sqrt(1-sin x)-sqrt(1+sin x)))

If y=(tan^(-1)(sqrt(1+sin x)+sqrt(1-sin x)))/(sqrt(1+sin x)-sqrt(1-sin x)) find the value of (dy)/(dx)

Prove the following: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x epsilon(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))

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-sinx)))=(x)/(2), x in (0, (pi)/(4)) .