Chapter 6.9, Problem 58ES

Prove the identities.

(a) $\cosh x+\sinh x=e^x$

(b) $\cosh x-\sinh x=e^{-x}$

(c) $\sinh \left(x+y\right)=\sinh x\cosh y+\cosh x\sinh y$

(d) $\sinh 2x=2\sinh x\cosh x$

(e) $\cosh \left(x+y\right)=\cosh x\cosh y+\sinh x\sinh y$

(f) $\cosh 2x={\cosh }^{2}x+{\sinh }^{2}x$

(g) $\cosh 2x=2{\sinh }^{2}x+1$

(h) $\cosh 2x=2{\cosh }^{2}x-1$