Choose the one alternative that best completes the statement or answers the question.
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) $2 \sin \beta \cos \beta ( \sin \alpha - \cos \alpha )$

Question

Quizplus · Accepted Answer

The expression $\sin ( \alpha + \beta ) \cos \beta - \cos ( \alpha + \beta ) \sin \beta$ simplifies to $\sin \alpha$ based on the sine difference formula, $\sin(\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$, where $\alpha$ is replaced by $\alpha + \beta$ and $\beta$ by $\beta$, simplifying to $\sin \alpha$.

Choose the One Alternative That Best Completes the Statement or Answers