Edexcel AEA 2018 June — Question 2 7 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2018
SessionJune
Marks7
PaperDownload PDF ↗
TopicQuadratic trigonometric equations
TypeShow then solve: tan/sin/cos identity manipulation
DifficultyChallenging +1.8 This AEA question requires recognizing a compound angle pattern (sin 47° cos³x + cos 47° sin x cos²x), factoring out cos²x, applying the sin(A+B) identity to get sin(47°+x)cos²x = ½cos²x, then solving the resulting cases. It demands pattern recognition beyond standard A-level and careful handling of multiple solution branches, but follows a clear path once the key insight is found.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

2.Solve,for \(0 \leqslant x \leqslant 360 ^ { \circ }\) $$\sin 47 ^ { \circ } \cos ^ { 3 } x + \cos 47 ^ { \circ } \sin x \cos ^ { 2 } x = \frac { 1 } { 2 } \cos ^ { 2 } x$$

2.Solve,for $0 \leqslant x \leqslant 360 ^ { \circ }$

$$\sin 47 ^ { \circ } \cos ^ { 3 } x + \cos 47 ^ { \circ } \sin x \cos ^ { 2 } x = \frac { 1 } { 2 } \cos ^ { 2 } x$$

\hfill \mbox{\textit{Edexcel AEA 2018 Q2 [7]}}