| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Disprove statement by counterexample |
| Difficulty | Moderate -0.3 Part (i) is trivial—any simple values like A=B=0 or A=B=45° provide a counter-example with basic calculator work. Part (ii) is a standard trigonometric identity proof requiring routine manipulation (converting to sin/cos, common denominator, double angle formula) that appears in most C3 textbooks. The 7 total marks reflect length rather than conceptual difficulty, making this slightly easier than average overall. |
| Spec | 1.01c Disproof by counter example1.05l Double angle formulae: and compound angle formulae1.05p Proof involving trig: functions and identities |
\begin{enumerate}[label=(\roman*)]
\item Prove, by counter-example, that the statement
"$\sec(A + B) = \sec A + \sec B$, for all $A$ and $B$"
is false. [2]
\item Prove that
$$\tan \theta + \cot \theta = 2 \cosec 2\theta, \quad \theta \neq \frac{n\pi}{2}, n \in \mathbb{Z}.$$ [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q4 [7]}}