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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 $$x$$.

i.e.
$\cosh x=\frac{e^x+e^{-x}}{2}$ $\sinh x=\frac{e^x-e^{-x}}{2}$

Note by Rushi Jogdand
3 months ago