(a) Demonstrate that the equation \(\sqrt{5} \sec x + \tan x = 4\) can be rewritten as \(R \cos(x + \alpha) = \sqrt{5}\), where \(R > 0\) and \(0^\circ < \alpha < 90^\circ\). Provide the exact value of \(R\) and the value of \(\alpha\) to two decimal places.

(b) Solve the equation \(\sqrt{5} \sec 2x + \tan 2x = 4\) for \(0^\circ < x < 180^\circ\).