Find the simplest form of `tan^(-1)(sqrt((1-sin x)/(1+sin x))),0 lt x lt pi`

Simplify tan^(-1)(sqrt((1-sin x)/(1+sin x))), 0lt x ltpi

Write the following function in the simplest form: tan^(-1)((cos x-sin x)/(cos x+sin x)),x

Write the simplest form : tan^-1( (cos x)/(1+sin x))

Write each of the following in the simplest form: (i) sin^(-1){(sqrt(1+x)+sqrt(1-x))/2},\ \ 0 < x <1 (ii) sin{2tan^(-1)(sqrt((1-x)/(1+x)))}

Write the simplest form : cot^(-1) [(sqrt(1+sinx)+sqrt(1-sin x))/(sqrt(1+sinx)-sqrt(1-sin x)]], x epsilon [0, pi/4]

y = sin ^(-1)((1 - x^(2))/(1+ x^(2))) 0 lt x lt 1

Solve : tan^(-1)((cos x)/(1+sin x)) , -(pi)/(2) lt x lt (pi)/(2)

If f(x) = tan^(-1)(sqrt((1+sinx)/(1-sinx))), 0 lt x lt pi/2 , then f'(pi/6) is

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)))

Write simplest form: sin^(-1)(x^(2)sqrt(1-x^(2))+x sqrt(1-x^(4)))