Question

Обчисліть
1) arccos(-1) + 2arccos 1/2
2)arccos1-п
3)arcsin(-1/2) - arccos √3/2
4) arcsin 1/2 + arccos (-√3/2)
5) arcsin1 + arccos(-1)
6) arccos (-√2/2) - arccos √2/2

Answer 1

$1)arcCos(-1)+2arcCosfrac{1}{2}=pi +frac{pi }{3}=frac{4pi }{3}\\2)arcCos1-pi=0-pi=-pi \\3)arcSin(-frac{1}{2})-arcCosfrac{sqrt{3} }{2}=-frac{pi }{6}-frac{pi }{6}=-frac{2pi }{6}=-frac{pi }{3}$

$4)arcSinfrac{1}{2}+arcCos(-frac{sqrt{3} }{2})=frac{pi }{6}+frac{5pi }{6}=frac{6pi }{6}=pi\\5)arcSin1+arcCos(-1)=frac{pi }{2}+pi=frac{3pi }{2}\\6)arcCos(-frac{sqrt{2} }{2})-arcCosfrac{sqrt{2} }{2}=frac{3pi }{4}-frac{pi }{4}=frac{2pi }{4}=frac{pi }{2}$