int_(0)^(1)(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))}=(pi)/(2)-(x)/(2)," if "(pi)/(2)

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

Prove that: *cot^(^^)(-1){(sqrt(1+sin x)+sqrt(1-sin x)/(sqrt(1+sin x)-sqrt(1-sin x))}=pi/2-x/2,| ifpil 2

show that , cot ^(-1) {(sqrt(1+sin x)+sqrt(1- sin x))/( sqrt(1+sin x)- sqrt(1-sin x))}=(x)/(2),0 lt x lt (pi)/(2)

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))

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

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