(a)[3]
Rewrite $4\cos \theta + 3\sin \theta$ as $R\cos(\theta - \alpha)$, with $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$. State the value of $\alpha$ correct to 4 decimal places.
(b(i))[4]
Hence determine the solutions of the equation $4\cos \theta + 3\sin \theta = 2$ for $0 < \theta < 2\pi$.
(b(ii))[3]
Hence evaluate $\int \frac{50}{(4\cos \theta + 3\sin \theta)^2} \, d\theta$.