| Exam Board | Edexcel |
|---|---|
| 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 (a) is a standard trigonometric identity proof using double angle formulas (1-cos2θ = 2sin²θ, sin2θ = 2sinθcosθ), requiring routine algebraic manipulation. Part (b) applies this identity to solve an equation, requiring substitution and solving a quadratic in tanθ, then finding exact solutions in a given range. This is a typical C3 trigonometry question with standard techniques and no novel insight required, making it slightly easier than average. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\alph*)]
\item Prove that
$$\frac{1 - \cos 2\theta}{\sin 2\theta} \equiv \tan \theta, \quad \theta \neq \frac{n\pi}{2}, n \in \mathbb{Z}.$$ [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 Q6 [9]}}