Subtraction Formulas for Hyperbolic Functions

Theorem

Hyperbolic Sine of Difference

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

Hyperbolic Cosine of Difference

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

Hyperbolic Tangent of Difference

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

Hyperbolic Cotangent of Difference

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

Also see

• Addition Formulas for Hyperbolic Functions

• Subtraction Formulas
• Addition Formulas