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