Prove that $\sin^2 2\theta (\cosec^2 \theta - \sec^2 \theta)$ simplifies to $4 \cos 2\theta$.
(ii(a))[4]
Hence, for $0^\circ < \theta \leq 180^\circ$, solve the equation $\sin^2 2\theta (\cosec^2 \theta - \sec^2 \theta) = 3$.
(ii(b))[2]
Find the exact value of $\cosec^2 15^\circ - \sec^2 15^\circ$, using exact trigonometric values.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the relations $\cosec \theta = \frac{1}{\sin \theta}$ and $\sec \theta = \frac{1}{\cos \theta}$” …