(a)[5]
Prove that $\sin 2\theta (\cosec \theta - \sec \theta)$ can be transformed into $\sqrt{8} \cos \left(\theta + \frac{\pi}{4}\right)$.
(b)[2]
Solve $\sin 2\theta (\cosec \theta - \sec \theta) = 1$ for $0 < \theta < \frac{1}{2}\pi$, giving your answer to $3$ significant figures.
(c)[3]
Find $\int \sin x (\cosec \tfrac{1}{2}x - \sec \tfrac{1}{2}x) \, dx$.