Hyperbolic Sine of Sum/Corollary

Corollary of Hyperbolic Sine of Sum

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

where $\sinh$ denotes the hyperbolic sine and $\cosh$ denotes the hyperbolic cosine.


Proof

\(\ds \map \sinh {a - b}\) \(=\) \(\ds \sinh a \map \cosh {-b} + \cosh a \map \sinh {-b}\) Hyperbolic Sine of Sum
\(\ds \) \(=\) \(\ds \sinh a \cosh b - \cosh a \sinh b\) Hyperbolic Cosine Function is Even and Hyperbolic Sine Function is Odd

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 8$: Hyperbolic Functions: $8.20$: Addition Formulas
  • 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $5$
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