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

Simplify :sin[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+cosx)/(1-cosx))) , 0< x < pi

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

sqrt((1-tan x)/(1+tan 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)))}

Find the simplified value of- y=tan^-1(sqrt((1-x)/(1+x)))

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

Simplify : ( sqrt( 1 + x^2 ) + sqrt( 1 - x^2 ) ) /( sqrt( 1 + x^2 ) - sqrt( 1 - x^2 ) )