| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Prove trigonometric identity |
| Difficulty | Moderate -0.3 This is a standard trigonometric identity proof requiring knowledge that 1 + tan²θ = sec²θ and the double angle formula cos 2θ = cos²θ - sin²θ. The proof follows a routine path: rewrite in terms of sin and cos, simplify, and apply the double angle formula. Slightly easier than average as it's a bookwork-style proof with a clear method that students practice regularly. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae |
Prove that
$$\frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = \cos 2\theta.$$ [4]
\hfill \mbox{\textit{Edexcel C3 Q30 [4]}}