| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Prove identity with double/compound angles |
| Difficulty | Moderate -0.8 This is a straightforward question testing standard double angle formulae recall (parts a(i) and a(ii)), followed by a routine algebraic verification (part b) and a standard trigonometric equation (part c). All components are textbook exercises requiring direct application of memorized formulae with minimal problem-solving insight, making it easier than the average A-level question. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
4
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Express $\sin 2 x$ in terms of $\sin x$ and $\cos x$.
\item Express $\cos 2 x$ in terms of $\cos x$.
\end{enumerate}\item Show that
$$\sin 2 x - \tan x = \tan x \cos 2 x$$
for all values of $x$.
\item Solve the equation $\sin 2 x - \tan x = 0$, giving all solutions in degrees in the interval $0 ^ { \circ } < x < 360 ^ { \circ }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2006 Q4 [9]}}