Question

Express the product $\cos \left(4\theta \right)\cos \left(2\theta \right)$as a sum containing only sines or only cosines.

Short answer

$\cos 4\theta \cos 2\theta =\frac{\cos 6\theta +\cos 2\theta }{2}$

Step-by-step solution

Step 1. Given expression 

$\cos \left(4\theta \right)\cos \left(2\theta \right)$

Step 2. Rewriting the expression    

$$\begin{gathered} 2\cos A\cos B=\cos (A+B)+\cos (A-B) \\ so, \\ \cos 4\theta \cos 2\theta =\frac{\cos 6\theta +\cos 2\theta }{2} \end{gathered}$$