Question 4 - A-Level Maths

Express \(( \sqrt { } 6 ) \sin x + \cos x\) in the form \(R \sin ( x + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). State the exact value of \(R\) and give \(\alpha\) correct to 3 decimal places.
Hence solve the equation \(( \sqrt { } 6 ) \sin 2 \theta + \cos 2 \theta = 2\), for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).