| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/1 (Pre-U Further Mathematics Paper 1) |
| Year | 2013 |
| Session | November |
| Marks | 5 |
| Topic | Complex numbers 2 |
| Type | De Moivre to derive trigonometric identities |
| Difficulty | Standard +0.3 This is a standard application of de Moivre's theorem requiring expansion of (cos θ + i sin θ)³, equating real parts, and using cos²θ = 1 - sin²θ to eliminate sin²θ terms. The deduction requires substituting θ = 2x and factoring, which is routine algebraic manipulation. While it involves multiple steps, these are well-practiced techniques for Further Maths students with no novel insight required. |
| Spec | 1.05l Double angle formulae: and compound angle formulae4.02q De Moivre's theorem: multiple angle formulae |
Use de Moivre's theorem to express $\cos 3\theta$ in terms of powers of $\cos \theta$ only, and deduce the identity $\cos 6x \equiv \cos 2x(2\cos 4x - 1)$. [5]
\hfill \mbox{\textit{Pre-U Pre-U 9795/1 2013 Q2 [5]}}