The ratio of number $2$ to subtraction of the negative natural exponential function from the positive natural exponential function is called the hyperbolic cosecant function.

$e$ is a positive irrational mathematical constant and take $x$ as a variable. The positive and negative natural exponential functions are written in mathematics as $e^x$ and $e^{-x}$ respectively.

The subtraction of the negative natural exponential function from positive natural exponential function is $e^x-e^{-x}$

The ratio of the quantity $2$ to the subtraction of them is written mathematically as follows.

$\large \dfrac{2}{e^x-e^{-x}}$

In mathematics, the ratio of $2$ to the subtraction of the natural exponential functions is called the hyperbolic co-secant function. It is denoted by either ${\mathop{\rm cosech}\nolimits}$ or ${\mathop{\rm csch}\nolimits}$ but the function is expressed in terms of $x$. Therefore, the hyperbolic cosecant function is written as ${\mathop{\rm cosech}\nolimits}{x}$ or ${\mathop{\rm csch}\nolimits}{x}$ mathematically.

$\large {\mathop{\rm csch}\nolimits}{x} \,=\, \dfrac{2}{e^x-e^{-x}}$

Latest Math Topics

Nov 11, 2022

Nov 03, 2022

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

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

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

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

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved