Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

(a)[3]

Show that $\sin 2\theta \cot \theta - \cos 2\theta = 1$.

(b)[2]

Hence determine the exact value of $\sin \frac{\pi}{6} \cot \frac{\pi}{12}$.

(c)[2]

Find the least positive value of $\theta$ (in radians) that satisfies $\sin 2\theta \cot \theta - 3 \cos 2\theta = 1$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use at least two of $\sin2\theta=2\sin\theta\cos\theta$, $\cos2\theta=\cos^2\theta-\sin^2\theta$, $\cot\theta=\dfrac{\cos\theta}{\sin\theta}$” …

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