Use the sum-to-product formulas to write the given expression as a product. $\cos 8 \theta - \cos 6 \theta$
A) $- 2 \sin 7 \theta \sin \theta$
B) $2 \cos 7 \theta \cos \theta$
C) $2 \cos 7 \theta \sin \theta$
D) $2 \sin 7 \theta \cos \theta$
E) $- 2 \cos 7 \theta \cos \theta$

Question

Quizplus · Accepted Answer

The sum-to-product formula for cosine is given by $\cos A - \cos B = -2 \sin \left(\frac{A + B}{2}\right) \sin \left(\frac{A - B}{2}\right)$. Applying this to $\cos 8\theta - \cos 6\theta$, we get $-2 \sin(7\theta) \sin(\theta)$, which matches choice A.

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