| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Quadratic trigonometric equations |
| Type | Show then solve: tan/sin/cos identity manipulation |
| Difficulty | Challenging +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. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
2.Solve,for $0 \leqslant x \leqslant 360 ^ { \circ }$
$$\sin 47 ^ { \circ } \cos ^ { 3 } x + \cos 47 ^ { \circ } \sin x \cos ^ { 2 } x = \frac { 1 } { 2 } \cos ^ { 2 } x$$
\hfill \mbox{\textit{Edexcel AEA 2018 Q2 [7]}}