Question

$2arcsin( - \frac{ \sqrt{3} }{2} ) + arctg( - 1) + arccos \sqrt{ \frac{2}{2} }$
$3arcsin \frac{1}{2} + 4arccos ( - \frac{ \sqrt{1} }{2} ) - arcctg( - \sqrt{3)}$
ДАМ 30 БАЛЛОВ ПОМОГИТЕ
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Answer 1

Ответ:

$\displaystyle 2arcsin(-\frac{\sqrt3}{2})+arctg(-1)+arccos\frac{\sqrt2}{2}=-2\cdot \frac{\pi}{3}-\frac{\pi}{4}+\frac{\pi}{4}=-\frac{2\pi}{3}\\\\\\\\3arcsin\frac{1}{2}+4\, arccos(-\frac{1}{\sqrt2})-arcctg(-\sqrt3)=3\cdot \frac{\pi}{6} +4\cdot (\pi -\frac{\pi}{4})-(\pi -\frac{\pi}{6})=\\\\\\=\frac{\pi}{2}+3\pi -\frac{5\pi}{6}=\frac{16\pi}{6}=\frac{8\pi}{3}$