Prove that: `tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2`

Explanation

`cot^-1 (1/x) = tan^-1 x`

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

as we know `tan^-1 x + tan^-1 y = tan^-1((x+y)/(1-xy))`

so, `tan^-1(((1-x^2)/(2x) + (2x)/(1-x^2))/(1- (1-x^3)/(2x)xx(2x)/(1-x^2)))`

`= tan^-1(oo) = pi/2`

hence proved