7. (a) Express \(\sin x + \sqrt { 3 } \cos x\) in the form \(R \sin ( x + \alpha )\), where \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\).
(b) Show that the equation \(\sec x + \sqrt { 3 } \operatorname { cosec } x = 4\) can be written in the form $$\sin x + \sqrt { 3 } \cos x = 2 \sin 2 x$$ (c) Deduce from parts (a) and (b) that \(\sec x + \sqrt { 3 } \operatorname { cosec } x = 4\) can be written in the form $$\sin 2 x - \sin \left( x + 60 ^ { \circ } \right) = 0$$ END