Prove that the identity $2\sin\theta \cosec 2\theta \equiv \sec\theta$ is true.
(b)[5]
Solve the equation $\tan^2\theta + 7\sin\theta \cosec 2\theta = 8$ within $-\pi < \theta < \pi$.
(c)[3]
Find the integral $\int 8\sin^2\frac{1}{2}x \, \cosec^2 x\, dx$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Express the left-hand side in terms of $\sin\theta$ and $\cos\theta$ by using $\csc 2\theta=\frac{1}{\sin 2\theta}$” …