Mjc 2010 H2 Math Prelim Verified [exclusive] Jun 2026
Solution: $\cos 2\theta = \sin \theta$ $\Rightarrow 1 - 2\sin^2 \theta = \sin \theta$ $\Rightarrow 2\sin^2 \theta + \sin \theta - 1 = 0$ $\Rightarrow (2\sin \theta - 1)(\sin \theta + 1) = 0$ $\Rightarrow \sin \theta = \frac12 \text or \sin \theta = -1$ $\Rightarrow \theta = 30^\circ, 150^\circ, 270^\circ$
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Often framed as a word problem (e.g., finding a three-digit number based on digit properties). Maclaurin Series: Expanding functions like and comparing terms with other series. Graph Sketching: Solution: $\cos 2\theta = \sin \theta$ $\Rightarrow 1

