1. (i) Show that , $Rsin$$( \theta + \alpha )\equivR$  $cos \alpha$ $sin \theta +R$ $sin \alpha$ $cos \theta$ where $R$ and $\alpha$ are constants with $R>0$ and $0< \alpha <\frac{ \pi }{2}$.

(ii) Use your result from part (i) to show that $\sqrt{3}sin \theta +cos \theta \equiv2sin( \theta +\frac{ \pi }{6})$.