| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Solve equation using proven identity |
| Difficulty | Standard +0.3 This question requires proving a standard double-angle identity using known formulas (straightforward algebraic manipulation), then solving a trigonometric equation by substitution. While it involves multiple steps and careful algebraic work, both parts follow routine procedures without requiring novel insight—slightly easier than average for A-level. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
Question 5:
5
2tanθ
tan2θ=
1−tan2θ
1 1−tan2θ
cot2θ= = *
tan2θ 2tanθ
1−tan2θ
=1+tanθ
2tanθ
1−tan2θ=2tanθ+2tan2θ
3tan2θ+2tanθ−1=0
(3tanθ−1)(tanθ+1)=0Show that $\cot 2\theta = \frac{1 - \tan^2 \theta}{2 \tan \theta}$.
Hence solve the equation
$$\cot 2\theta = 1 + \tan \theta \quad \text{for } 0° < \theta < 360°.$$ [7]
\hfill \mbox{\textit{OCR MEI C4 Q5 [7]}}