Question 6 - A-Level Maths

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