(a)[3]
Show that $3\tan^2\theta + 5\sin^2\theta$ can be written as $\dfrac{8\sin^2\theta - 5\sin^4\theta}{1 - \sin^2\theta}$.
(b)[4]
Hence solve $3\tan^2\theta + 5\sin^2\theta = 9$ for $0^\circ < \theta < 270^\circ$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
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This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Replace $\tan^2\theta$ by $\frac{\sin^2\theta}{\cos^2\theta}$” …
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