What is $$\sin \alpha - \sin \beta$$?

A

$$2\cos \frac{\alpha + \beta}{2} \sin \frac{\alpha - \beta}{2}$$

B

$$2\sin \frac{\alpha + \beta}{2} \sin \frac{\alpha - \beta}{2}$$

C

$$2\cos \frac{\alpha - \beta}{2} \sin\frac{\alpha + \beta}{2}$$

D

$$2\cos \frac{\alpha + \beta}{2} \cos \frac{\alpha - \beta}{2}$$