$$ -\frac{\pi}{2}\leq arcsin(x) \leq \frac{\pi}{2}, \,\,\,arcsin(-x)=-arcsin(x), $$

$$ 0\leq arccos(x) \leq \pi,\,\,\,arccos(-x)=\pi-arccos(x), $$

$$ -\frac{\pi}{2}\leq arctg(x) \leq \frac{\pi}{2},\,\,\,arctg(-x)=-arctg(x), $$

$$ 0\leq arcctg(x) \leq \pi,\,\,\,arcctg(-x)=\pi-arcctg(x), $$

$$ arcsin(x)=\frac{\pi}{2}-arccos(x)=arctg\left(\frac{x}{\sqrt{1-x^2}}\right), $$

$$ arccos(x)=\frac{\pi}{2}-arcsin(x)=arcctg\left(\frac{x}{\sqrt{1-x^2}}\right), $$

$$ arctg(x)=\frac{\pi}{2}-arcctg(x)=arcsin\left(\frac{x}{\sqrt{1+x^2}}\right), $$

$$ arcctg(x)=\frac{\pi}{2}-arctg(x)=arccos\left(\frac{x}{\sqrt{1+x^2}}\right), $$

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