(a)[2]
Prove that $2\sin\theta \cosec 2\theta \equiv \sec\theta$.
(b)[5]
Solve the equation $\tan^2\theta + 7\sin\theta\cosec 2\theta = 8$ for $-\pi < \theta < \pi$.
(c)[3]
Find $\displaystyle \int 8\sin^2\!\left(\dfrac{x}{2}\right)\cosec^2 x\, dx$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rewrite the left-hand side in terms of $\sin\theta$ and $\cos\theta$ by using $\cosec2\theta=\frac{1}{\sin2\theta}$” …
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