Establish the Identity $$\sin \left( x - \frac { \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } ( \sin x - \cos x )$$

Establish the identity.
- $$\sin \left( x - \frac { \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } ( \sin x - \cos x )$$