| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Solve equation using proven identity |
| Difficulty | Standard +0.3 Part (a) is a standard trigonometric identity proof requiring routine manipulation of cot, cosec, and cos definitions—straightforward for A-level students. Part (b) requires substituting the proven identity and solving a trigonometric equation, which involves algebraic manipulation and finding solutions in a given range. While it requires multiple steps and careful algebra, the techniques are standard and the question provides scaffolding through part (a), making it slightly easier than average overall. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
In this question you must show detailed reasoning.
\begin{enumerate}[label=(\alph*)]
\item Prove that $(\cot \theta + \cosec \theta)^2 = \frac{1 + \cos \theta}{1 - \cos \theta}$. [4]
\item Hence solve, for $0 < \theta < 2\pi$, $3(\cot \theta + \cosec \theta)^2 = 2 \sec \theta$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2019 Q5 [9]}}