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Hyperbolic cosine function


$\large \cosh{x} \,=\, \dfrac{e^{\displaystyle x}+e^{\displaystyle -x}}{2}$


The ratio of the summation of $e$ raised to the power of positive real number and $e$ raised to the power of negative real number to the number $2$ is called the hyperbolic cosine function. Here $e$ is a mathematical constant, well known as Napier’s constant.

The term hyperbolic cosine is abbreviated as $\cosh$ mathematically. If $x$ is a literal number and represents a real number, the hyperbolic cosine function is expressed as $\cosh{x}$ in mathematics.


The definition of the hyperbolic cosine function is written in the following mathematical form.

$\cosh{x} \,=\, \dfrac{e^x+e^{-x}}{2}$

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