| Exam Board | Edexcel |
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| Module | FP3 (Further Pure Mathematics 3) |
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| Year | 2017 |
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| Session | June |
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| Topic | Hyperbolic functions |
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3. (a) Using the definition for \(\cosh x\) in terms of exponentials, show that
$$\cosh 2 x \equiv 2 \cosh ^ { 2 } x - 1$$
(b) Find the exact values of \(x\) for which
$$29 \cosh x - 3 \cosh 2 x = 38$$
giving your answers in terms of natural logarithms.