| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Prove trigonometric identity |
| Difficulty | Moderate -0.3 Part (i) is a straightforward application of a double angle formula (cos 2x = 1 - 2sin²x) followed by finding the reciprocal, requiring only standard manipulation. Part (ii) is a routine trigonometric identity proof using standard double angle formulas and algebraic simplification. Both parts are typical C3 exercises with no novel insight required, making this slightly easier than the average A-level question which would typically involve more problem-solving or integration of multiple concepts. |
| Spec | 1.05h 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 formulae1.05p Proof involving trig: functions and identities |
\begin{enumerate}[label=(\roman*)]
\item Given that $\sin x = \frac{3}{5}$, use an appropriate double angle formula to find the exact value of $\sec 2x$. [4]
\item Prove that
$$\cot 2x + \cosec 2x \equiv \cot x, \quad \left(x \neq \frac{n\pi}{2}, n \in \mathbb{Z}\right).$$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q5 [8]}}