Question

ВЫЧИСЛИТЬ ЗНАЧЕНИЕ ОБРАТНОЙ ТРИГОНОМЕТРИЧЕСКОЙ ФУНКЦИИ

Answer 1

1)  $arccos(-1)+arcsinleft(-frac{sqrt{2}}{2}right)+arctan(-1)-arctan(-sqrt{3})=$

$=pi-frac{pi}{4}-frac{pi}{4}-(-frac{pi}{3})=pi-frac{pi}{2}+frac{pi}{3}=$

$=frac{pi}{2}+frac{pi}{3}=frac{5pi}{6}$

2)$arccosleft(-frac{sqrt{2}}{2}right)*arctanleft(-frac{1}{sqrt{3}}right)-arcsinleft(-frac{1}{2}right)*arccotleft(-frac{1}{sqrt{3}}right)=$

$=-frac{pi}{4}*(-frac{pi}{6})-left(-frac{pi}{6}right)*(-frac{pi}{3})=frac{pi}{4}*frac{pi}{6}-frac{pi}{6}*frac{pi}{3}=$

$=frac{pi^2}{6}*(frac{1}{4}-frac{1}{3})= frac{pi^2}{6}*(- frac{1}{12} )=-frac{pi^2}{72}$