सिद्ध कीजिए कि `tan^(-1)""{(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=(pi)/(4)-(1)/(2)cos^(-1)x , 0 lt x lt 1`

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

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)

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

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

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

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