Use the sum-to-product formulas to rewrite the sum or difference as a product. $\sin 9 \theta + \sin 7 \theta$
A) $2 \sin 8 \theta \sin \theta$
B) $2 \cos 8 \theta \cos \theta$
C) $2 \sin 8 \theta \cos \theta$
D) $2 \cos 8 \theta \sin \theta$
E) $2 \sin 9 \theta \cos 7 \theta$

Question

Use the sum-to-product formulas to rewrite the sum or difference as a product.   $\sin 9 \theta + \sin 7 \theta$  
A)  $2 \sin 8 \theta \sin \theta$
B)  $2 \cos 8 \theta \cos \theta$
C)  $2 \sin 8 \theta \cos \theta$  
D)  $2 \cos 8 \theta \sin \theta$
E)  $2 \sin 9 \theta \cos 7 \theta$

Quizplus · Accepted Answer

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

Use the Sum-To-Product Formulas to Rewrite the Sum or Difference sin⁡9θ+sin⁡7θ\sin 9 \theta + \sin 7 \thetasin9θ+sin7θ

Use the Sum-To-Product Formulas to Rewrite the Sum or Difference $\sin 9 \theta + \sin 7 \theta$