[11)tan^(1)((sqrt(1+x)-sqrt(1-y))/(sqrt(1+x)+sqrt(1-x)))^((1)/(4))-(1)/(2)cos^(-1)x],[" Det "]

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

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

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

prove tan ^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2 cos ^(-1) x, -1/2 le x le 1

If y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))), find (dy)/(dx)

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

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-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x =1/(sqrt(2))ltxle1