xcos^-1(x^2-1/x^2+1)+tan^-1(2x/1-x^2) please solve it

Question

this question is of class 12

Answer 1

Let θ=cos^-1((x²-1)/(x²+1)), so (x²-1)/(x²+1)=cosθ making tanθ=2x/(x²-1) (Pythagoras). 

(We have a right triangle with hypotenuse length =x²+1 and the other two side lengths are 2x and x²-1.)

So tan(-θ)=-tanθ=2x/(1-x²). Therefore tan^-1(2x/(1-x²)=-θ.

The given expression becomes xθ-θ or θ(x-1). If x=1 the expression becomes zero.