| Exam Board | Edexcel |
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| Module | FP3 (Further Pure Mathematics 3) |
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| Year | 2010 |
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| Session | June |
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| Topic | Hyperbolic functions |
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3. (a) Starting from the definitions of \(\sinh x\) and \(\cosh x\) in terms of exponentials, prove that
$$\cosh 2 x = 1 + 2 \sinh ^ { 2 } x$$
(b) Solve the equation
$$\cosh 2 x - 3 \sinh x = 15$$
giving your answers as exact logarithms.