tan^(-1)[(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))]=alpha

Solve for x:tan^(-1)[(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))]=beta

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)

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) .

If tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))))=theta , then prove that, sin 2 theta=x^(2) .

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

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)