" 6."sqrt((1+sin x)/(1-sin x))

The values of x in [-2 pi,2 pi], for which the graph of the function y=sqrt((1+sin x)/(1-sin x))-sec x and y=-sqrt((1-sin x)/(1+sin x)) coincide are

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)

If y=tan^(-1)sqrt((1-sin x)/(1+sin x)), then the value of (dy)/(dx) at x=(pi)/(6) is.

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

(cot^(-1){sqrt(1+sin x)+sqrt(1-sin x)})/(sqrt(1+sin x)-sqrt(1-sin x))

Find the value of 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))]=

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