11. If $\tan x \cdot \tan y=2, \sin x \cdot \sin y=\frac{1}{3}$, then $x-y$ $=$
$$
\text { II, } 11.2 k \pi \pm \frac{\pi}{3} \text {. }
$$

Given $\tan x \cdot \tan y=2, \sin x \cdot \sin y=\frac{1}{3}$
$$
\begin{array}{l}
\Rightarrow \cos x \cdot \cos y=\frac{1}{6} \\
\Rightarrow \cos (x-y)=\frac{1}{2} \\
\Rightarrow x-y=2 k \pi \pm \frac{\pi}{3} .
\end{array}
$$