Solve equation with combined sin2x and cos2x

Solve a trigonometric equation of the form a sin2x + b cos2x = c (with both sin2x and cos2x present), typically by using R sin(2x + α) or dividing to get tan2x = k.

3 questions · Standard +0.0

1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
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CAIE P1 2006 June Q2
4 marks Moderate -0.8
2 Solve the equation $$\sin 2 x + 3 \cos 2 x = 0$$ for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).
OCR MEI C4 2016 June Q4
5 marks Moderate -0.3
4 Solve the equation \(2 \sin 2 \theta = 1 + \cos 2 \theta\) for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).
Edexcel AEA 2006 June Q2
10 marks Challenging +1.2
2.Given that \(( \sin \theta + \cos \theta ) \neq 0\) ,find all the solutions of $$\frac { 2 \cos 2 \theta ( \sin 2 \theta - \sqrt { } 3 \cos 2 \theta ) } { \sin \theta + \cos \theta } = \sqrt { } 6 ( \sin 2 \theta - \sqrt { } 3 \cos 2 \theta )$$ for \(0 \leq \theta < 360 ^ { \circ }\) .