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

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

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

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

tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}

The derivative of tan^(-1)((sqrt(1 + x)-sqrt(1-x))/(sqrt(1 + x)+sqrt(1-x))) is

Prove that: *cot^(^^)(-1){(sqrt(1+sin x)+sqrt(1-sin x)/(sqrt(1+sin x)-sqrt(1-sin x))}=pi/2-x/2,| ifpil 2

tan^-1 (sqrt(x)+sqrt(a))/(1-sqrt(x)sqrt(a))