Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

(a)[3]

Prove that $$\frac{\tan \theta + 7}{\tan^2 \theta - 3} = \frac{\sin \theta \cos \theta + 7 \cos^2 \theta}{1 - 4 \cos^2 \theta}$$ is an identity.

(b)[4]

Hence solve the equation $$\frac{\sin \theta \cos \theta + 7 \cos^2 \theta}{1 - 4 \cos^2 \theta} = \frac{5}{\tan \theta}$$ for $0^\circ \leq \theta \leq 180^\circ$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Rewrites $\tan\theta$ as $\frac{\sin\theta}{\cos\theta}$, or uses an equivalent identity

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