| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.3 This is a straightforward hyperbolic equation requiring substitution of definitions (cosh x = (e^x + e^-x)/2, sinh x = (e^x - e^-x)/2), simplification to a quadratic in e^x, and solving to give x = ln(something). While it's a Further Maths topic, the method is standard and mechanical with no conceptual difficulty beyond knowing the definitions, making it slightly easier than average overall. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials |
Find the values of $x$ for which
$$4 \cosh x + \sinh x = 8,$$
giving your answer as natural logarithms. [6]
\hfill \mbox{\textit{Edexcel FP3 Q10 [6]}}