| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2020 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Prove trigonometric identity |
| Difficulty | Standard +0.3 This is a straightforward trigonometric identity proof requiring standard techniques: expanding the compound angle formula for cos(2θ + 45°), applying the double angle formula cos(2θ) = cos²θ - sin²θ, and recognizing sin(2θ) = 2sinθcosθ. The √2 factor comes naturally from cos 45° = sin 45° = 1/√2. While it requires knowing several identities, the path is direct with no novel insight needed, making it slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae |
Prove that $\sqrt{2} \cos(2\theta + 45°) = \cos^2 \theta - 2\sin \theta \cos \theta - \sin^2 \theta$, where $\theta$ is measured in degrees. [3]
\hfill \mbox{\textit{OCR H240/02 2020 Q6 [3]}}