Half Angle Formulas/Hyperbolic Tangent

Theorem
Let $x \in \R$.

Then:

where $\tanh$ denotes hyperbolic tangent and $\cosh$ denotes hyperbolic cosine.

Proof
We also have that:
 * when $x \ge 0$, $\tanh \dfrac x 2 \ge 0$
 * when $x \le 0$, $\tanh \dfrac x 2 \le 0$.

Also see

 * Half Angle Formula for Hyperbolic Sine
 * Half Angle Formula for Hyperbolic Cosine