已知 $\cos \left(\alpha-\frac{\pi}{4}\right)=\frac{1}{4}$, 则 $\sin 2 \alpha=$
解析: $\because \cos \left(\alpha-\frac{\pi}{4}\right)=\frac{1}{4}$ ，

$\therefore 2 \cos ^{2}\left(\alpha-\frac{\pi}{4}\right)-1=2 \times \frac{1}{16}-1=-\frac{7}{8}=\cos \left(2 \alpha-\frac{\pi}{2}\right)=\cos \left(\frac{\pi}{2}-2 \alpha\right)=\sin 2 \alpha$.

答案: D