tan^(-1)(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))<=x<=1

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)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1

Show that tan^-1(frac{sqrt(1+x)-sqrt(1-x)}{sqrt(1+x)+sqrt(1-x)})=pi/4-1/2cos^-1 x

Show that tan^-1(frac{sqrt(1+x)-sqrt(1-x)}{sqrt(1+x)+sqrt(1-x)}) = frac{pi}{4}-frac{1}{2}cos^-1x , for -frac{1}{sqrt2} le x le1

Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))} with respect to cos^(-1)x^2

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha, then prove that x^2=sin2alpha

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha, then prove that x^2=sin2alpha

If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) then prove that x^(2) = sin 2alpha .