Hyperbolic Cosine of Zero is One

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
\(\ds \) \(=\) \(\ds 1\)

$\blacksquare$


Also see

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