若 $\sin \alpha \cdot \sin \beta=1$, 则 $\cos (\alpha-\beta)$ 的值为( B )
析] $\because \sin \alpha \sin \beta=1, \therefore\left\{\begin{array}{l}\sin \alpha=-1 \\ \sin \beta=-1\end{array}\right.$ 或 $\left\{\begin{array}{l}\sin \alpha=1 \\ \sin \beta=1\end{array}\right.$,

由 $\cos ^{2} \alpha+\sin ^{2} \alpha=1$ 得 $\cos \alpha=0$,

$\therefore \cos (\alpha-\beta)=\cos \alpha \cdot \cos \beta+\sin \alpha \cdot \sin \beta=0+1=1$.