Show that the equation \(\sqrt { 5 } \sec x + \tan x = 4\) can be expressed as \(R \cos ( x + \alpha ) = \sqrt { 5 }\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the exact value of \(R\) and the value of \(\alpha\) correct to 2 decimal places. [4]
Hence solve the equation \(\sqrt { 5 } \sec 2 x + \tan 2 x = 4\), for \(0 ^ { \circ } < x < 180 ^ { \circ }\).