Prove that `sec x+tan x=sqrt((1+sin x)/(1-sin x))`

Prove that sec x-cos x=tan x sin x

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

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),0

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

Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqrt(1-sin x))] = x/2, x in (0, pi/4)