| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2007 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Prove identity then solve equation |
| Difficulty | Standard +0.3 This is a straightforward two-part question: proving a standard double-angle identity using sec²θ = 1 + tan²θ and cos2θ = cos²θ - sin²θ, then solving a simple equation by setting sec2θ = 2. Both parts require only routine manipulation of well-known identities with no novel insight, making it slightly easier than average. |
| Spec | 1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
Show that $\frac{1+\tan^2\theta}{1-\tan^2\theta} \equiv \sec 2\theta$.
Hence, or otherwise, solve the equation $\frac{1+\tan^2\theta}{1-\tan^2\theta} = 2$, for $0° \leq \theta \leq 180°$. [7]4 Show that $\frac { 1 + \tan ^ { 2 } \theta } { 1 - \tan ^ { 2 } \theta } = \sec 2 \theta$.\\
Hence, or otherwise, solve the equation $\frac { 1 + \tan ^ { 2 } \theta } { 1 - \tan ^ { 2 } \theta } = 2$, for $0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C4 2007 Q4 [7]}}