# Formulas of Inverse Hyperbolic Functions

1. $Sin{h^{ – 1}}x = {\log _e}\left| {x + \sqrt {{x^2} + 1} } \right|$
2. $Cos{h^{ – 1}}x = {\log _e}\left| {x + \sqrt {{x^2} – 1} } \right|{\text{ }}x \geqslant 1$
3. $Tan{h^{ – 1}}x = \frac{1}{2}{\log _e}\left| {\frac{{1 + x}}{{1 – x}}} \right|{\text{ }}{x^2} < 1$
4. $Cot{h^{ – 1}}x = \frac{1}{2}{\log _e}\left| {\frac{{x + 1}}{{x – 1}}} \right|{\text{ }}{x^2} > 1$
5. $Sec{h^{ – 1}}x = {\log _e}\left| {\frac{{1 + \sqrt {1 – {x^2}} }}{x}} \right|{\text{ }}\left| x \right| < 0$
6. $Co\sec {h^{ – 1}}x = {\log _e}\left| {\frac{{1 + \sqrt {1 + {x^2}} }}{x}} \right|{\text{ }}\left| x \right| < 0$
7. $Tan{h^{ – 1}}x = Sin{h^{ – 1}}\left( {\frac{x}{{\sqrt {1 – {x^2}} }}} \right)$