| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve using sech/tanh identities |
| Difficulty | Standard +0.8 This is a Further Maths question requiring knowledge of hyperbolic identities (sech²x + tanh²x = 1) and substitution techniques to convert to a quadratic in e^x. While the algebraic manipulation is substantial, the method is standard for FP3 hyperbolic equation questions, making it moderately challenging but not exceptional. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07c Hyperbolic identity: cosh^2(x) - sinh^2(x) = 1 |
\begin{enumerate}
\item Solve the equation
\end{enumerate}
$$7 \operatorname { sech } x - \tanh x = 5$$
Give your answers in the form $\ln a$, where $a$ is a rational number.\\
\hfill \mbox{\textit{Edexcel FP3 Q1 [6]}}