" 37."sqrt(((1+sin x)/(1-sin x)))[CBSE1996C]

Tan ^(-1) (sqrt ((1 - sin x )/( 1 + sin x )))

Derivative of y=(sqrt((1-sin x)/(1+sin x))) is

(d)/(dx ) {sqrt((1+sin x )/(1-sin x ))}=

(d)/(dx) [ 2 cot^(-1) ((sqrt(1+ sin x) + sqrt(1-sin x))/(sqrt(1+ sin x) - sqrt(1-sin x)))]=

If y= sqrt ((1+sin x) /( 1-sin x) ,)then (dy)/(dx) =

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))

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

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