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

• Hyperbolic Sine of Zero is Zero