Write the product as a sum. $\cos 7 x \cos 3 x$
A) $\cos 7 x + \cos 3 x$
B) $[ \cos 7 x + \cos 3 x ] / 2$
C) $[ \cos 10 x + \cos 4 x ] / 2$
D) $- [ \cos 10 x + \cos 2 x ] / 2$
E) none of these

Question

Quizplus · Accepted Answer

We can use the product-to-sum identity for cosine:
$$\cos a \cos b = \frac{\cos(a+b)+\cos(a-b)}{2}$$
Setting $a=7x$ and $b=3x$, we have:
$$\cos 7x \cos 3x = \frac{\cos(7x+3x)+\cos(7x-3x)}{2} = \frac{\cos 10x + \cos 4x}{2}$$ 
Therefore, the answer is choice C.

Write the Product as a Sum cos⁡7xcos⁡3x\cos 7 x \cos 3 xcos7xcos3x

Write the Product as a Sum $\cos 7 x \cos 3 x$