已知 $0<\alpha<\frac{\pi}{2}<\beta<\pi, \cos \alpha=\frac{3}{5}, \sin (\alpha+\beta)=-\frac{3}{5}$, 则 $\cos \beta$ 的值为()
$\because 0<\alpha<\frac{\pi}{2}, \frac{\pi}{2}<\beta<\pi, \therefore \frac{\pi}{2}<\alpha+\beta<\frac{3}{2} \pi$,

$\therefore \sin \alpha=\frac{4}{5}, \cos (\alpha+\beta)=-\frac{4}{5}, \quad \therefore \cos \beta=\cos [(\alpha+\beta)-\alpha]$ $=\cos (\alpha+\beta) \cos \alpha+\sin (\alpha+\beta) \sin \alpha=\left(-\frac{4}{5}\right) \times \frac{3}{5}+\left(-\frac{3}{5}\right) \times \frac{4}{5}=-\frac{24}{25}$, 故选 C.