Hyperbolic Cosine of Zero is One
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Theorem
- $\map \cosh 0 = 1$
where $\cosh$ denotes the hyperbolic cosine.
Proof
\(\ds \map \cosh 0\) | \(=\) | \(\ds \dfrac {e^0 + e^{-0} } 2\) | Definition of Hyperbolic Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {1 + 1} 2\) | Definition of Integer Power | |||||||||||
\(\ds \) | \(=\) | \(\ds 1\) |
$\blacksquare$