Show that, by using trigonometric identities, $4\sin\left(\theta + \frac{1}{3}\pi\right)\cos\left(\theta - \frac{1}{3}\pi\right) = \sqrt{3} + 2\sin 2\theta$.
(b)[2]
Find the exact value of $4\sin\frac{17\pi}{24}\cos\frac{\pi}{24}$.
(c)[4]
Find the exact value of $\int_{0}^{\frac{3\pi}{8}} 4\sin(2x + \frac{1}{3}\pi)\cos(2x - \frac{1}{3}\pi)\, dx$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Derive at least one of $\tfrac12 \sin \theta + \tfrac{\sqrt3}{2} \cos \theta$ or $\tfrac12 \cos \theta + \tfrac{\sqrt3}{2} \sin \theta$” …