Direct solve: tanθ equation factorisation

A question is this type if and only if it asks directly to solve an equation involving tanθ (including tanθ=2sinθ or similar) by writing tanθ=sinθ/cosθ and factorising, with no prior 'show' part required.

6 questions · Standard +0.0

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
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CAIE P1 2023 June Q1
3 marks Moderate -0.3
1 Solve the equation \(4 \sin \theta + \tan \theta = 0\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).
OCR MEI C2 Q4
3 marks Moderate -0.3
4 Find the values of \(\theta\) such that \(0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }\) which satisfy the equation $$\cos \theta \tan \theta = \frac { \sqrt { 3 } } { 2 }$$
OCR MEI C2 Q6
4 marks Moderate -0.3
6 Solve the equation \(\tan \theta = 2 \sin \theta\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
OCR MEI C2 2011 June Q7
4 marks Moderate -0.3
7 Solve the equation \(\tan \theta = 2 \sin \theta\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
OCR MEI AS Paper 2 2020 November Q8
6 marks Standard +0.3
8 In this question you must show detailed reasoning.
Solve the equation \(3 \cos \theta + 8 \tan \theta = 0\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\), giving your answers correct to the nearest degree.
Edexcel AEA 2014 June Q2
6 marks Challenging +1.2
Given that $$3\sin^2 x + 2\sin x = 6\cos x + 9\sin x \cos x$$ and that \(-90° < x < 90°\), find the possible values of \(\tan x\). [6]