| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 6 |
| Topic | Trig Proofs |
| Type | Solve equation using proven identity |
| Difficulty | Standard +0.3 Part (a) is a standard trigonometric identity proof requiring knowledge of double angle formulas and tan-to-sin/cos conversion—routine for A-level. Part (b) requires substituting the proven identity and solving sin 2θ = 3cos 2θ, which is straightforward using tan 2θ = 3 and inverse tan. This is a typical multi-part question with standard techniques, slightly above average due to the two-part structure and need to connect the identity to the equation, but no novel insight required. |
| 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 |
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac{2\tan\theta}{1 + \tan^2\theta} = \sin 2\theta$. [3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
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\item In this question you must show detailed reasoning.
Solve $\frac{2\tan\theta}{1 + \tan^2\theta} = 3\cos 2\theta$ for $0 \leq \theta \leq \pi$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2017 Q8 [6]}}