(a)[5]
After expanding $\cos(x - 60^{\circ})$, demonstrate that $2\cos(x - 60^{\circ}) + \cos x$ can be expressed in the form $R\cos(x - \alpha)$, where $R > 0$ and $0^{\circ} < \alpha < 90^{\circ}$. State the exact value of $R$ and give $\alpha$ correct to 2 decimal places.
(b)[2]
Hence determine the value of $x$ in the interval $0^{\circ} < x < 360^{\circ}$ for which $2\cos(x - 60^{\circ}) + \cos x$ attains its least possible value.