Express the Product as a Sum or Difference $$\sin \frac { x } { 2 } \cos \frac { 9 x } { 2 }$$

Multiple Choice

Express the product as a sum or difference.
- $$\sin \frac { x } { 2 } \cos \frac { 9 x } { 2 }$$

A) $\frac { 1 } { 2 } ( \sin 5 x - \sin 4 x )$
B) $\frac { 1 } { 4 } ( \cos 10 x - \sin 8 x )$
C) $\frac { 1 } { 4 } \sin ( \cos 9 x )$
D) $\frac { 1 } { 2 } ( \cos 5 x + \sin 4 x )$