- (a) Express \(5 \cos 2 \theta - 12 \sin 2 \theta\) in the form \(R \cos ( 2 \theta + \alpha )\), where \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\) Give the value of \(\alpha\) to 2 decimal places.
(b) Hence solve, for \(0 \leqslant \theta < 180 ^ { \circ }\), the equation
$$5 \cos 2 \theta - 12 \sin 2 \theta = 10$$
giving your answers to 1 decimal place.