Express the product as a sum containing only sines or cosines.
-$2 \cos ( 7 \theta ) \cos \theta$
A) $\cos ( 10 \theta ) + \sin ( 4 \theta )$
B) $\cos ( 14 \theta ) + \cos ( 2 \theta )$
C) $\cos ( 8 \theta ) + \cos ( 6 \theta )$
D) $\cos ( 8 \theta ) + \sin ( 6 \theta )$

Question

Quizplus · Accepted Answer

The product-to-sum formula for cosines is $\cos A \cos B = \frac{1}{2}[\cos(A - B) + \cos(A + B)]$. Applying this to $2 \cos(7\theta) \cos(\theta)$, we get $\cos(7\theta - \theta) + \cos(7\theta + \theta)$ which simplifies to $\cos(6\theta) + \cos(8\theta)$.

Express the Product as a Sum Containing Only Sines or Cosines