`tan^(-1) [ (√1+x - √1-x)/(√1+x + √1-x)] = π/4 - 1/2 cos^-1 x`

Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

If x != 0 , then tan((pi)/4 + 1/2 cos^(-1) x) + tan ((pi)/4 - 1/2 cos^(-1) x) = ......

Is tan^(-1) (sqrt((1-x^(2))/(1+x^(2))) ) = 1/2 cos^(-1) x true ?

tan ^ (- 1) ((cos x) / (1-tan x))

tan ^ (- 1) ((cos x-sin x) / (cos x + sin x)) = tan ^ (- 1) ((1-tan x) / (1 + tan x))

cot {tan ^ (- 1) x + tan ^ (- 1) ((1) / (x))} + cos ^ (- 1) (1-2x ^ (2)) + cos ^ (- 1) ( 2x ^ (2) -1) = pi, x> 0

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2 cos^(-1)x , 0