| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Prove trigonometric identity |
| Difficulty | Moderate -0.3 This is a standard trigonometric identity proof requiring knowledge of the double angle formula for cosine and the identity sec²θ = 1 + tan²θ. While it requires multiple steps (expressing in terms of sin/cos, simplifying, and recognizing the double angle formula), it follows a routine approach typical of C3 identity proofs with no novel insight needed. |
| 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
$$\frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = \cos 2\theta$$
[6]
\hfill \mbox{\textit{Edexcel C3 Q4 [6]}}