Show that $\cos 3\theta = 4\cos^3 \theta - 3\cos \theta$.[3] Hence, or otherwise, evaluate \(

Question

Show that $\cos 3\theta = 4\cos^3 \theta - 3\cos \theta$.[3] Hence, or otherwise, evaluate $\displaystyle \displaystyle\int_0^{\frac{\pi}{6}} \sin 2\theta \cos 3\theta \, \mathrm{d}\theta$ exactly.[4]

Accepted Answer

(a) Shown. (b) $\dfrac{3\sqrt3}{10}-\dfrac25$

2025 ASRJC P1 Q2

2025 ASRJC P1 Q2

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