. 已知 $\tan \alpha=2$. (1)求 $\tan \left(\alpha+\frac{\pi}{4}\right)$ 的值;(2)求 $\frac{\sin 2 \alpha}{\sin ^{2} \alpha+\sin \alpha \cos \alpha-\cos 2 \alpha-1}$ 的值.
(1) $\tan \left(\alpha+\frac{\pi}{4}\right)=\frac{\tan \alpha+\tan \frac{\pi}{4}}{1-\tan \alpha \tan \frac{\pi}{4}}=\frac{2+1}{1-2 \times 1}=-3$.(2) $\frac{\sin 2 \alpha}{\sin ^{2} \alpha+\sin \alpha \cos \alpha-\cos 2 \alpha-1}$$=\frac{2 \sin \alpha \cos \alpha}{\sin ^{2} \alpha+\sin \alpha \cos \alpha-\left(2 \cos ^{2} \alpha-1\right)-1}$$=\frac{2 \sin \alpha \cos \alpha}{\sin ^{2} \alpha+\sin \alpha \cos \alpha-2 \cos ^{2} \alpha}$$=\frac{2 \tan \alpha}{\tan ^{2} \alpha+\tan \alpha-2}$$=\frac{2 \times 2}{2^{2}+2-2}$$=1$.