Show that :`2tan^(-1)x+sin^(-1)((2x)/(1+x^2))` is constant for `xgeq1,` find that constant.

Explanation

`=pi−sin^( −1) ( frac{2x}((1+x)^2})+sin ^(−1) (frac{2x/((1+x )^2} )`

When `x=1`,

`=2tan^(-1)1+sin^(-1)(2/(1+1^2))`

`=2tan^(-1)1+sin^(-1)1`

`=pi/2 +(pi/2)`

`=pi`