Find the values of the following
`tan frac(1)(2) [sin^(-1)((2x)/(1+x^2))+ cos^(-1) ((1-y^2)/(1+y^2))],|x| lt 1, y gt 0 and x y lt 1`

Explanation

Given expression
`tan frac(1)(2)[2 tan^(-1) x + 2 tan^(-1) y]`
`tan(tan^(-1) x + tan^(-1) y)`
`tan[tan^(-1) ((x+y)/(1-xy))] = (x+y)/(1_xy)`