If `sin^(-1)((2a)/(1+a^(2))) + cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((2x)/(1-x^(2)))`, where `a, x in]0,1[`, then the value of x is

Explanation

We have given

`sin^(-1)((2a)/(1+a^(2))) + cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((2x)/(1-x^(2)))`

Then

`2tan^(−1)a−2tan^(−1)b=2tan^(−1)x`

`tan^(−1)a−tan^(−1)b=tan^(−1)x`

`tan^(−1)((a-b)/(1+ab))=tan^(-1)x`

`x=(a-b)/(1+ab)`