Question

If $\tan ^{-1} x+\tan ^{-1} y=\frac{\pi}{4}, x y<1$, then write the value of $x+y+x y$.

Answer 1

SOLUTION : $\tan ^{-1} x+\tan ^{-1} y=\frac{\pi}{4} \quad$ if $x y<1$

$\tan ^{-1}\left(\frac{x+y}{1-x y}\right)=\frac{\pi}{4}  \Rightarrow  \frac{x+y}{1-x y}=\tan \frac{\pi}{4} \\$

$x+y=1-x y  \Rightarrow  x+y+x y=1$