" Q."1quad " If "y=tan^(-1)[(sqrt(1+x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))-sqrt(1-x^(2))]" prove that "x^(2)=sin2y

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)=sin2 alpha

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 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) =sin 2alpha .

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 .

If y=tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))] for 0<|x|<1 ,find (dy)/(dx)

If y=tan^-1frac{sqrt(1+x^2)+sqrt(1-x^2)}{sqrt(1+x^2)-sqrt(1-x^2)] , show that x^2=sin 2y

If y=tan^(-1)[(x-sqrt(1-x^(2)))/(x+sqrt(1-x^(2)))]," then "(dy)/(dx)=