Complete the Identity $\sin ( \alpha + \beta ) \cos \beta - \cos ( \alpha + \beta ) \sin \beta = ?$

Complete the identity.
- $\sin ( \alpha + \beta ) \cos \beta - \cos ( \alpha + \beta ) \sin \beta = ?$

A) $\sin \alpha \cos \beta - \cos \alpha \sin \beta$
B) $\sin \alpha \cos ^ { 2 } \beta - \sin \alpha \sin ^ { 2 } \beta$
C) $\sin \alpha$
D) $2 \sin \beta \cos \beta ( \sin \alpha - \cos \alpha )$

Correct Answer:

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