Use the sum-to-product formulas to write the given expression as a product. $\sin 9 \theta - \sin 7 \theta$
A) $2 \sin 8 \theta \cos \theta$
B) $2 \cos 8 \theta \cos \theta$
C) $- 2 \sin 8 \theta \sin \theta$
D) $- 2 \cos 8 \theta \cos \theta$
E) $2 \cos 8 \theta \sin \theta$

Question

Quizplus · Accepted Answer

The sum-to-product formula for $\sin A - \sin B$ is $2 \cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)$. Here, $A = 9\theta$ and $B = 7\theta$, so the expression becomes $2 \cos 8\theta \sin \theta$.

Use the Sum-To-Product Formulas to Write the Given Expression as a Product