Answer
$-1$
Work Step by Step
Recall that:
$\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\cos(\alpha)\sin(\beta)$
Hence,
$\sin(\frac{\pi}{12})\cos(\frac{7\pi}{12})-\cos(\frac{\pi}{12})\sin(\frac{7\pi}{12})=\sin\left(\frac{\pi}{12}-\frac{7\pi}{12}\right)=\sin(-\frac{\pi}{2})=-1.$
