[y=tan^(-1)[(sqrt(1+sin x))/(sqrt(1+tan x))-sqrt(1-sin x)]],[(pi)/(2)

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1

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

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+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x)]] where 0 lt x lt pi/2 find (dy)/(dx)

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)

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

Differentiate 'tan^(^^)(-1){(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))},darr backslash0