Simplify : `s i n[2tan^(- 1)sqrt((1-x)/(1+x))]`

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

Simplify "tan"^(-1)[sqrt((1-"cos"x)/(1+"cos"x))],xltpi .

y=tan^(- 1)sqrt((1-x)/(1+x))f i n d(dy)/(dx)

y=tan^(- 1)sqrt((1-x)/(1+x))f i n d(dy)/(dx)

tan^(-1)(x+sqrt(1+x^(2)))=

Simplify y=tan^(-1)(x/(1+sqrt(1-x^2)))

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)))}