Addition Formulas for Hyperbolic Functions

Theorem

$\map \sinh {a + b} = \sinh a \cosh b + \cosh a \sinh b$

$\map \cosh {a + b} = \cosh a \cosh b + \sinh a \sinh b$

$\map \tanh {a + b} = \dfrac {\tanh a + \tanh b} {1 + \tanh a \tanh b}$

$\map \coth {a + b} = \dfrac {\coth a \coth b + 1} {\coth b + \coth a}$

However, it is the view of $\mathsf{Pr} \infty \mathsf{fWiki}$ that the arguments of the hyperbolic functions are in general not actually angles as they frequently are for the Compound Angle Formulas, and hence is a misnomer.