| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Solve equation using proven identity |
| Difficulty | Standard +0.3 Part (i) is direct recall worth 1 mark. Part (ii) is a standard identity proof requiring substitution of the double angle formula and algebraic manipulation. Part (iii) requires combining the proven identity with the given equation, leading to a quadratic in tan x, then solving—this is routine C3 trigonometry with multiple steps but follows standard patterns. Overall slightly above average difficulty due to the multi-step nature and 9 total marks, 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=(\roman*)]
\item Write down the formula for $\cos 2x$ in terms of $\cos x$. [1]
\item Prove the identity $\frac{4 \cos 2x}{1 + \cos 2x} = 4 - 2 \sec^2 x$. [3]
\item Solve, for $0 < x < 2\pi$, the equation $\frac{4 \cos 2x}{1 + \cos 2x} = 3 \tan x - 7$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q7 [9]}}