已知 $\cos \alpha=\frac{3}{5}, \cos (\alpha+\beta)=-\frac{5}{13}, \alpha 、 \beta$ 都是锐角, 则 $\cos \beta=(\mathrm{C})$
析] $\because \alpha 、 \beta$ 是锐角, $\therefore 0<\alpha+\beta<\pi$, 又 $\cos (\alpha+\beta)=-\frac{5}{13}<0, \therefore \frac{\pi}{2}<\alpha+\beta<\pi, \therefore \sin (\alpha+\beta)=\frac{12}{13}, \sin \alpha=$ $\frac{4}{5}$. 又 $\cos \beta=\cos (\alpha+\beta-\alpha)=\cos (\alpha+\beta) \cos \alpha+\sin (\alpha+\beta) \sin \alpha=-\frac{5}{13} \times \frac{3}{5}+\frac{12}{13} \times \frac{4}{5}=\frac{33}{65}$.