(i)[3]
Prove the identity that $\sin(x - 30^{\circ}) + \cos(x - 60^{\circ}) = (\sqrt{3})\sin x$.
(ii)[6]
Hence solve the equation $\sin(x - 30^{\circ}) + \cos(x - 60^{\circ}) = \frac{1}{2}\sec x$, in the interval $0^{\circ} < x < 360^{\circ}$.
Mathematics 9709 · AS & A Level · Trigonometry