Hyperbolic Sine of Zero is Zero

Theorem

$\map \sinh 0 = 0$

where $\sinh$ denotes the hyperbolic sine.


Proof

\(\ds \map \sinh 0\) \(=\) \(\ds \dfrac {e^0 - e^{-0} } 2\) Definition of Hyperbolic Sine
\(\ds \) \(=\) \(\ds \dfrac {1 - 1} 2\) Definition of Integer Power
\(\ds \) \(=\) \(\ds 0\)

$\blacksquare$


Also see

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