| Exam Board | Edexcel |
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| Module | F3 (Further Pure Mathematics 3) |
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| Year | 2021 |
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| Session | October |
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| Topic | Hyperbolic functions |
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2. Given that
$$\cosh y = x \quad \text { and } \quad y < 0$$
use the definition of coshy in terms of exponential functions to prove that
$$y = \ln \left( x - \sqrt { x ^ { 2 } - 1 } \right)$$