Establish the Identity $$\frac { \sin x + \cos x } { \sin x - \cos x } = \frac { 1 + 2 \sin x \cos x } { 2 \sin ^ { 2 } x - 1 }$$

Essay

Establish the identity.
- $$\frac { \sin x + \cos x } { \sin x - \cos x } = \frac { 1 + 2 \sin x \cos x } { 2 \sin ^ { 2 } x - 1 }$$