| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Disprove statement by counterexample |
| Difficulty | Standard +0.3 Part (i) is straightforward - students just need to substitute simple values like A=B=0 or A=B=45° to show the identity fails. Part (ii) is a standard trigonometric identity proof requiring manipulation of tan and cot into sin/cos form, then using the double angle formula for sin(2θ). While it requires multiple steps and knowledge of standard identities, this is a routine C3 proof with no novel insight needed, making it slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01c Disproof by counter example1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae |
\begin{enumerate}[label=(\roman*)]
\item Prove, by counter-example, that the statement
"$\sec(A + B) \equiv \sec A + \sec B$, 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 Q5 [7]}}