Chapter 11.10, Problem 49E

Use the definitions $\sinh x=\frac{e^x-e^{-x}}{2}\cosh x=\frac{e^x+e^{-x}}{2}$ and the Maclaurin series for $e^x$ to show that

(a) $\sinh x={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^{2n+1}}{(2n+1)!}}$

(b) $\cosh x={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^{2n}}{(2n)!}}$