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)