(a)[4]
Show that $\sqrt{5}\sec x + \tan x = 4$ may be written as $R\cos(x + \alpha) = \sqrt{5}$, with $R > 0$ and $0^\circ < \alpha < 90^\circ$. State the exact value of $R$ and give $\alpha$ correct to 2 decimal places.
(b)[4]
Hence determine the solutions of the equation $\sqrt{5}\sec 2x + \tan 2x = 4$, for $0^\circ < x < 180^\circ$.