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)`.

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

If y="tan"^(-1)(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) , then the value of (dy)/(dx) is -

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)))

y= tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))) , where -1 < x < 1 , find dy/dx

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) .

f(x)=sqrt(1-sin^(2)x)+sqrt(1+tan^(2)x) then

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

int_(1)^(2)(sqrt(x)dx)/(sqrt(x)+sqrt(3-x))=(1)/(2)

Show that the derivative of (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) w.r.t. sqrt(1-x^(4)) is (sqrt(1-x^(4))-1)/(x^(6)) .

If (x+sqrt(x^2-1))/(x-sqrt(x^2-1))+(x-sqrt(x^2-1))/(x+sqrt(x^2-1))= 14 ,then find the value of x.