Question

If tan^-1x+tan^-1y=π/4,xy<1, then write the value of x+y+xy.

Answer 1

Here, `tan^(−1) x+tan^(−1) y=π/4, xy < 1.`

`tan^(-1)((x+y)/(1-xy))=pi/4`

`(x+y)/(1−xy)=1`

`x+y=1−xy`

`x+y+xy=1`

Therefore, the value of x + y + xy is 1.