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Hyperbolic Function

Every function \(f(x)\) can be written uniquely as sum of an odd part and an even part.

\[f(x) = \frac{f(x)+f(-x)}{2} + \frac{f(x) - f(-x)}{2}\] \[\therefore e^{x}=\frac{e^x+e^{-x}}{2}+\frac{e^x-e^{-x}}{2}\] The even and odd terms are called as hyperbolic cosine and hyperbolic sine function of \(x\).

\[\cosh x=\frac{e^x+e^{-x}}{2}\] \[\sinh x=\frac{e^x-e^{-x}}{2}\]

Note by Rushi Jogdand
6 months, 2 weeks ago

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