Hyperbolic Identities

${\cosh }^{2}x-{\sinh }^{2}x=1$ $1-{\tanh }^{2}x=sec{h}^{2}x$ $\sinh (x+y)=\sinh x\cosh y+\cosh x\sinh y$ $\cosh (x+y)=\cosh x\cosh y+\sinh x\sinh y$