Formulas of Trigonometric and Logarithmic Functions

1) \[Sinx = \frac{{{e^{ix}} – {e^{ – ix}}}}{{2i}}\]

2) \[Cosx = \frac{{{e^{ix}} + {e^{ – ix}}}}{2}\]

3) \[Tanx = \frac{{{e^{ix}} – {e^{ – ix}}}}{{i({e^{ix}} + {e^{ – ix}})}}\]

4) \[Cotx = \frac{{i({e^{ix}} + {e^{ – ix}})}}{{{e^{ix}} – {e^{ – ix}}}}\]

5) \[Secx = \frac{2}{{{e^{ix}} + {e^{ – ix}}}}\]

6) \[Co\sec x = \frac{{2i}}{{{e^{ix}} – {e^{ – ix}}}}\]

7) \[Log(x + iy) = Log\sqrt {{x^2} + {y^2}} + iTa{n^{ – 1}}\left( {\frac{y}{x}} \right)\]

8) \[Log\left( {\frac{{x + iy}}{{x – iy}}} \right) = 2iTa{n^{ – 1}}\left( {\frac{y}{x}} \right)\]