Đẳng thức hàm số lượng giác nghịch

$\arcsin (x) = \int_{0}^{x} \frac{1}{\sqrt{1 - t^{2}}} d t = - i \log (i x + \sqrt{1 - x^{2}})$
$\arccos (x) = \frac{π}{2} - \arcsin (x) = \frac{π}{2} - \int_{0}^{x} \frac{1}{\sqrt{1 - t^{2}}} d t = \frac{π}{2} + i \log (i x + \sqrt{1 - x^{2}})$
$\arctan (x) = \int_{0}^{x} \frac{1}{1 + t^{2}} d t = \frac{i}{2} \log (\frac{1 - i x}{1 + i x})$
$arccsc (x) = \arcsin (\frac{1}{x}) = - i \log (\frac{i}{x} + \sqrt{1 - \frac{1}{z^{2}}})$
$arcsec (x) = \arccos (\frac{1}{x}) = \frac{π}{2} - \arcsin (\frac{1}{x}) = \frac{π}{2} + i \log (\frac{i}{x} + \sqrt{1 - \frac{1}{z^{2}}})$
$arccot (x) = \arctan (\frac{1}{x}) = \frac{π}{2} - \arctan (x) = \frac{π}{2} + \frac{i}{2} \log (\frac{1 + i x}{1 - i x})$
$\arcsin (x) + \arcsin (y) = \arcsin (x \sqrt{1 - y^{2}} + y \sqrt{1 - x^{2}})$
$\arccos (x) + \arccos (y) = \arccos (x y - \sqrt{(1 - x^{2}) (1 - y^{2})})$
$\arctan (x) + \arctan (y) = \arctan (\frac{x + y}{1 - x y}) (\mod π)$

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