# if

Question:

If $\tan ^{-1} x-\tan ^{-1} y=\frac{\pi}{4}$, then $x-y-x y=$  ____________________.

Solution:

$\tan ^{-1} x-\tan ^{-1} y=\frac{\pi}{4}$

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

$\Rightarrow \frac{x-y}{1+x y}=\tan \frac{\pi}{4}$

$\Rightarrow \frac{x-y}{1+x y}=1$

$\Rightarrow x-y=1+x y$

$\Rightarrow x-y-x y=1$

If $\tan ^{-1} x-\tan ^{-1} y=\frac{\pi}{4}$, then $x-y-x y=__1__.$