Show that $3\sin 2\theta \cot \theta = 6\cos^2 \theta$.
(b)[3]
Solve the equation $3\sin 2\theta \cot \theta = 5$ for values of $\theta$ in $0 < \theta < \pi$.
(c)[5]
Find the exact value of $\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} 3\sin x \, \cot \frac{1}{2}x \, dx$ for this integral.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply at least one of $\sin 2\theta = 2\sin\theta\cos\theta$ and $\cot\theta = \dfrac{\cos\theta}{\sin\theta}$” …