(i)[3]
By using the expansions of $\cos(3x+x)$ and $\cos(3x-x)$, demonstrate that $\frac{1}{2}(\cos 4x + \cos 2x) \equiv \cos 3x \cos x$.
(ii)[3]
Hence show that $\int_{-\frac{1}{6}\pi}^{\frac{1}{6}\pi} \cos 3x \cos x \, dx$ has value $\frac{3}{8}\sqrt{3}$.