| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2004 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Product of trig functions |
| Difficulty | Challenging +1.8 This AEA question requires recognizing that √(1 - ½sin2x) = √(sin²x + cos²x - sinxcosx) can be rewritten as √((sinx - cosx)²) = |sinx - cosx|, then solving cosx + |sinx - cosx| = 0 by considering cases based on the sign of (sinx - cosx). This demands algebraic insight beyond routine manipulation, careful case analysis, and checking solutions across the full interval, making it significantly harder than standard A-level trigonometry but not requiring the most extreme multi-stage reasoning of the hardest AEA problems. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
Solve the equation $\cos x + \sqrt{(1 - \frac{1}{2} \sin 2x)} = 0$, in the interval $0° \leq x < 360°$. [9]
\hfill \mbox{\textit{Edexcel AEA 2004 Q1 [9]}}