Edexcel AEA 2006 June — Question 2 10 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2006
SessionJune
Marks10
PaperDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeSolve equation with combined sin2x and cos2x
DifficultyChallenging +1.2 This is an AEA question requiring systematic algebraic manipulation of double angle formulae and factorization to solve a trigonometric equation. While it involves multiple steps (factoring out common terms, using double angle identities, and solving resulting equations), the approach is relatively standard once the factorization is spotted. The constraint and multiple solutions add some complexity, but this is more straightforward than typical AEA proof or geometric insight questions.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

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 \(0 \leq \theta < 360 ^ { \circ }\) .

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 $0 \leq \theta < 360 ^ { \circ }$ .

\hfill \mbox{\textit{Edexcel AEA 2006 Q2 [10]}}