Edexcel AEA 2013 June — Question 2 8 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2013
SessionJune
Marks8
PaperDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeSolve equation with tan(θ ± α)
DifficultyStandard +0.8 Part (a) is a straightforward proof using the sine addition formula. Part (b) requires manipulating the equation using trigonometric identities (recognizing tan form, using complementary angle relationships), then solving a quadratic in tan. While it's from AEA, this is a relatively accessible multi-step problem requiring solid technique but not exceptional insight—moderately above average difficulty.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
2.(a)Use the formula for \(\sin ( A - B )\) to show that \(\sin \left( 90 ^ { \circ } - x \right) = \cos x\) (b)Solve for \(0 < \theta < 360 ^ { \circ }\) $$2 \sin \left( \theta + 17 ^ { \circ } \right) = \frac { \cos \left( \theta + 8 ^ { \circ } \right) } { \cos \left( \theta + 17 ^ { \circ } \right) }$$ 
2.(a)Use the formula for $\sin ( A - B )$ to show that $\sin \left( 90 ^ { \circ } - x \right) = \cos x$\\
(b)Solve for $0 < \theta < 360 ^ { \circ }$

$$2 \sin \left( \theta + 17 ^ { \circ } \right) = \frac { \cos \left( \theta + 8 ^ { \circ } \right) } { \cos \left( \theta + 17 ^ { \circ } \right) }$$

\hfill \mbox{\textit{Edexcel AEA 2013 Q2 [8]}}
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