Solving $\cos(x)\cos(2x) = \cos(3x)$

Question

Are there specific trigonometric identities that I can use to solve the following problem: \begin{align*} \cos(x)\cos(2x) = \cos(3x) \end{align*}

Answer 1

HINT \begin{align*} \cos(3x) = \cos(x + 2x) = \cos(x)\cos(2x) - \sin(x)\sin(2x) \end{align*}

Answer 2

Hint:

$$\cos(\alpha)\cos(\beta)=\frac{1}{2}[\cos(\alpha+\beta)+\cos(\alpha-\beta)]$$

Apply that result to the LHS, as well as rewrite $\cos(3x)$ as $\cos(2x+x)$ and apply the above result.