| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Prove identity then find exact value and solve/integrate |
| Difficulty | Standard +0.8 This question requires applying compound angle formulas to expand two cosine expressions, then algebraically simplifying to prove an identity—a multi-step process requiring careful manipulation of surds. Part (ii) adds a further layer by requiring students to recognize how to substitute a specific value to extract cos 75°. While the techniques are standard C3 content, the algebraic complexity and the need to work backwards from the identity make this moderately harder than average. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.05g Exact trigonometric values: for standard angles1.05l Double angle formulae: and compound angle formulae |
\begin{enumerate}[label=(\roman*)]
\item Prove the identity
$$\sqrt{2} \cos (x + 45)° + 2 \cos (x - 30)° \equiv (1 + \sqrt{3}) \cos x°.$$ [4]
\item Hence, find the exact value of $\cos 75°$ in terms of surds. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q3 [7]}}