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 $x-y-x y=__1__.$
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