Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\sin 3 \theta - \sin \theta$$
A) $2 \sin 3 \theta \cos \theta$
B) $2 \sin 2 \theta \cos \theta$
C) $2 \cos 2 \theta \cos \theta$
D) $2 \sin 2 \theta \sin \theta$
E) $2 \cos 2 \theta \sin \theta$

Question

Use the sum-to-product formulas to rewrite the sum or difference as a product.​ $$\sin 3 \theta - \sin \theta$$ ​
A)​ $2 \sin 3 \theta \cos \theta$
B)​ $2 \sin 2 \theta \cos \theta$
C)​ $2 \cos 2 \theta \cos \theta$
D)​ $2 \sin 2 \theta \sin \theta$
E)​ $2 \cos 2 \theta \sin \theta$

Quizplus · Accepted Answer

The sum-to-product formula for $\sin A - \sin B$ is $2 \cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)$. Applying it to $\sin 3\theta - \sin \theta$, we get $2 \cos 2\theta \sin \theta$.

Use the Sum-To-Product Formulas to Rewrite the Sum or Difference sin⁡3θ−sin⁡θ\sin 3 \theta - \sin \thetasin3θ−sinθ

Use the Sum-To-Product Formulas to Rewrite the Sum or Difference $\sin 3 \theta - \sin \theta$