Formulas of Inverse Trigonometric Functions

1) $Si{n^{ – 1}}x = \frac{1}{i}Log(ix + \sqrt {1 – {x^2}} )$

2) $Co{s^{ – 1}}x = \frac{1}{i}Log(x + \sqrt {{x^2} – 1} )$

3) $Ta{n^{ – 1}}x = \frac{1}{{2i}}Log\left( {\frac{{1 + ix}}{{1 – ix}}} \right)$

4) $Co{t^{ – 1}}x = \frac{1}{{2i}}Log\left( {\frac{{x + i}}{{x – i}}} \right)$

5) $Se{c^{ – 1}}x = \frac{1}{i}Log\left( {\frac{{1 + \sqrt {1 – {x^2}} }}{x}} \right)$

6) $Co{\sec ^{ – 1}}x = \frac{1}{i}Log\left( {\frac{{i + \sqrt {{x^2} – 1} }}{x}} \right)$

7) $Ta{n^{ – 1}}\left( {\frac{{x + iy}}{{x – iy}}} \right) = \frac{\pi }{4} + \frac{i}{2}Log\left( {\frac{{x + y}}{{x – y}}} \right)$