Question

Calculate
$arc\sin (-\frac{\sqrt{2}}{2})+arc\cos (-\frac{1}{2})-arc\tan (-\sqrt{3})+arc\cot \left(\frac{1}{\sqrt{3}}\right)=?$

Answer 1

$arcsin(-\frac{\sqrt{2}}{2})+arccos(-\frac{1}{2})-arctan(-\sqrt{3})+arccot\left(\frac{1}{\sqrt{3}}\right)$

$=si{n}^{-1}(-\frac{1}{\sqrt{2}})+co{s}^{-1}(-\frac{1}{2})-ta{n}^{-1}(-\sqrt{3})+co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$=-\pi /4+\pi -\pi /3+\pi /3+\pi /3=\frac{13\pi }{12}$