| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Show equation reduces to tan form |
| Difficulty | Standard +0.3 Part (a) is a standard 'show that' proof using the double angle formula for sine and basic trigonometric identities (tan = sin/cos, sec² = 1 + tan²). Part (b) requires substituting the result from (a), applying the double angle formula for cosine, and solving a quadratic equation in sin θ. While it requires multiple steps and careful algebraic manipulation, the techniques are all standard A-level methods with no novel insight required. Slightly easier than average due to the scaffolding provided by part (a). |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
8
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac { 2 \tan \theta } { 1 + \tan ^ { 2 } \theta } = \sin 2 \theta$.
\item In this question you must show detailed reasoning.
Solve $\frac { 2 \tan \theta } { 1 + \tan ^ { 2 } \theta } = 3 \cos 2 \theta$ for $0 \leq \theta \leq \pi$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 Q8 [6]}}