Hyperbolic Function Identities

1. ${\cosh }^2(x)-{\sinh }^2(x)=1$
2. $\sinh (-x)=-\sinh (x)$
3. $\cosh (-x)=\cosh (x)$
4. $\cosh (x+y)=\cosh x\cosh y+\sinh x\sinh y$
5. $\sinh (x+y)=\sinh x\cosh y+\cosh x\sinh y$