若锐角 $\alpha, \beta$ 满足 $\cos \alpha=\frac{4}{5}, \cos (\alpha+\beta)=\frac{3}{5}$, 则 $\sin \beta$ 的值是（）
$\because \cos \alpha=\frac{4}{5}, \cos (\alpha+\beta)=\frac{3}{5}, \alpha, \beta \in\left(0, \frac{\pi}{2}\right), \therefore 0<\alpha+\beta<\frac{\pi}{2}$,

$\therefore \sin \alpha=\frac{3}{5}, \sin (\alpha+\beta)=\frac{4}{5}$,

$\therefore \sin \beta=\sin [(\alpha+\beta)-\alpha]=\sin (\alpha+\beta) \cos \alpha-\cos (\alpha+\beta) \sin \alpha=\frac{4}{5} \times \frac{4}{5}-\frac{3}{5} \times \frac{3}{5}$

$=\frac{7}{25}$,

故选 C.