Question

ВЫЧИСЛИТЬ ЗНАЧЕНИЕ ОБРАТНОЙ ТРИГОНОМЕТРИЧЕСКОЙ ФУНКЦИИ

Answer 1

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

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

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

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

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

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