Question 5 - A-Level Maths

Express \(\sqrt { 2 } \cos x - \sqrt { 5 } \sin x\) in the form \(R \cos ( x + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the exact value of \(R\) and the value of \(\alpha\) correct to 3 decimal places.
Hence solve the equation \(\sqrt { 2 } \cos 2 \theta - \sqrt { 5 } \sin 2 \theta = 1\), for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).