(i)[5]
First expand $\cos(x + 45^\circ)$, then write $\cos(x + 45^\circ) - (\sqrt{2})\sin x$ in the form $R\cos(x + \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$. State $R$ correct to 4 significant figures and $\alpha$ correct to 2 decimal places.
(ii)[4]
Hence solve the equation $\cos(x + 45^\circ) - (\sqrt{2})\sin x = 2$, for $0^\circ < x < 360^\circ$.