| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Solve equation using proven identity |
| Difficulty | Standard +0.3 Part (a) is a standard double-angle identity proof requiring straightforward application of cos 2θ = 1 - 2sin²θ and sin 2θ = 2sinθcosθ. Part (b) uses the proven result to solve an equation, requiring algebraic manipulation and careful consideration of the domain, but follows a predictable pattern. This is slightly easier than average as it's a routine C3 trigonometric proof and equation with standard techniques. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\alph*)]
\item Prove that
$$\frac{1 - \cos 2\theta}{\sin 2\theta} = \tan \theta, \quad \theta \neq \frac{n\pi}{2}, \quad n \in \mathbb{Z}.$$ [3]
\item Solve, giving exact answers in terms of $\pi$,
$$2(1 - \cos 2\theta) = \tan \theta, \quad 0 < \theta < \pi.$$ [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q8 [9]}}