User:Rushikeshjogdand1

Hyperbolic Functions
Every function $$f(x)$$ can be written in a unique way as composition of an even function and an odd functions — $$f(x)=\frac{f(x)+f(-x)}{2}+\frac{f(x)-f(-x)}{2}$$.

Similarly the exponential function $$e^x$$ can be displayed as — $$e^x=\frac{e^x+e^{-x}}{2}+\frac{e^x-e^{-x}}{2}$$. The even and odd parts are called as hyperbolic cosine and hyperbolic sine of $$x$$.

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