Math Doubts

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.

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

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved