10. 已知 $\cos \theta=-\frac{12}{13}, \theta \in\left(\pi, \frac{3 \pi}{2}\right)$, 求 $\cos \left(\theta+\frac{\pi}{4}\right)$ 的值.
$\cos \theta=-\frac{12}{13}, \theta \in\left(\pi, \frac{3 \pi}{2}\right)$ ，

$\therefore \sin \theta=-\frac{5}{13}$,

$\therefore \cos \left(\theta+\frac{\pi}{4}\right)=\cos \theta \cdot \cos \frac{\pi}{4}-\sin \theta \cdot \sin \frac{\pi}{4}$

$=-\frac{12}{13} \times \frac{\sqrt{2}}{2}-\left(-\frac{5}{13}\right) \times \frac{\sqrt{2}}{2}=-\frac{7 \sqrt{2}}{26}$.