Hyperbolic Cosine Function is Even

Theorem
Let $x \in \C$ be a complex number.

Let $\cosh x$ be the hyperbolic cosine of $x$.

Then:
 * $\cosh \left({-x}\right) = \cosh x$

That is, the hyperbolic cosine function is even.

Proof
Recall the definition of the hyperbolic cosine function:


 * $ \displaystyle \cosh x = \frac {e^{x} + e^{-x}} 2 $

Then,

Also see

 * Hyperbolic Sine Function is Odd
 * Hyperbolic Tangent Function is Odd
 * Cosine Function is Even