Prove that : `tan^-1[(sqrt(1+x) - sqrt(1-x))/(sqrt1+x + sqrt1-x)] = pi/4 - 1/2cos^-1x`

Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^2))] = pi/4 - 1/2cos^-1x^2

Prove that tan^-1((sqrt(1+x)- (sqrt(1-x)))/(sqrt(1+x) + (sqrt(1-x)))) = pi/4 - 1/2 cos^-1 x

Prove that : tan^-1[(sqrt(1+z) + sqrt(1-z))/(sqrt(1+z) - sqrt(1-z))= pi/4 + 1/2 cos^-1z

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)

Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)+(1)/(2)cos^(-1)x

Show that : tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=pi/4+1/2cos^(-1)x^(2) .

Show that: tan^(-1)[(sqrt(1+x^(2)) + sqrt(1-x^(2)))/(sqrt(1 +x^(2))- sqrt(1-x^(2)))]=pi/4 +1/2 cos^(-1) x^(2), -1 lt x lt 1

Prove that 2 tan^-1 sqrt((1- x)/(1+x))= x, -1 le x le 1

Differentiate tan^(-1) ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) w.r.t. x .