(a(i))[3]
Write $(\sqrt{3})\cos x + \sin x$ as $R \cos(x - \alpha)$, with $R > 0$ and $0 < \alpha < \tfrac{1}{2}\pi$, and state the exact values of $R$ and $\alpha$.
(a(ii))[4]
Thus show that $\displaystyle \int_{\pi/6}^{\pi/2} \frac{1}{((\sqrt{3})\cos x + \sin x)^2} \, dx = \tfrac{1}{4}\sqrt{3}$.