Hyperbolic Cosine of Sum/Corollary
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Corollary of Hyperbolic Cosine of Sum
- $\map \cosh {a - b} = \cosh a \cosh b - \sinh a \sinh b$
where $\sinh$ denotes the hyperbolic sine and $\cosh$ denotes the hyperbolic cosine.
Proof
\(\ds \map \cosh {a - b}\) | \(=\) | \(\ds \cosh a \map \cosh {-b} + \sinh a \map \sinh {-b}\) | Hyperbolic Sine of Sum | |||||||||||
\(\ds \) | \(=\) | \(\ds \cosh a \cosh b - \sinh a \sinh b\) | 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: $8.21$: Addition Formulas
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $5$