| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Solve equation with sin2x/cos2x by substitution |
| Difficulty | Challenging +1.2 This question requires applying double angle formulae (sin 2θ = 2sin θ cos θ, cos 2θ = 2cos²θ - 1), algebraic manipulation to form a quadratic in cos θ, and solving within a given domain. While it involves multiple steps and careful algebraic work, the approach is relatively standard for AEA level—identify the substitution, solve the quadratic, and find angles. It's more challenging than typical A-level due to the algebraic complexity and AEA context, but doesn't require exceptional insight. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
2.Solve,for $0 < \theta < 2 \pi$ ,
$$\sin 2 \theta + \cos 2 \theta + 1 = \sqrt { 6 } \cos \theta$$
giving your answers in terms of $\pi$ .
\hfill \mbox{\textit{Edexcel AEA 2005 Q2 [8]}}