Solution: $\cos 2\theta = \sin \theta$ $\Rightarrow 1 - 2\sin^2 \theta = \sin \theta$ $\Rightarrow 2\sin^2 \theta + \sin \theta - 1 = 0$ $\Rightarrow (2\sin \theta - 1)(\sin \theta + 1) = 0$ $\Rightarrow \sin \theta = \frac12 \text or \sin \theta = -1$ $\Rightarrow \theta = 30^\circ, 150^\circ, 270^\circ$
MJC 2010 H2 Math Prelim Solutions