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)

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