Question

Срочо!!!
Даю 30 балів!!!
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Answer 1

Ответ:

$1)\ \ arccos(-1)+2arccos\dfrac{1}{2}=(\pi -arccos1)+2\cdot \dfrac{\pi}{3}=\pi -0+\dfrac{2\pi }{3}=\dfrac{5\pi}{3}\\\\2)\ \ arccos1-\pi =0-\pi =-\pi \\\\3)\ \ arcsin\Big(-\dfrac{1}{2} \Big)-arccos\dfrac{\sqrt3}{2}=-\dfrac{\pi}{6}-\dfrac{\pi}{6}=-\dfrac{2\pi}{6}=-\dfrac{\pi}{3}\\\\4)\ \ arcsin\dfrac{1}{2}+arccos\Big(-\dfrac{\sqrt3}{2}\Big)=\dfrac{\pi}{6}+\Big(\pi -arccos\dfrac{\sqrt3}{2}\Big)=\dfrac{\pi}{6}+\pi -\dfrac{\pi}{6}=\pi$

$5)\ \ arcsin1+arccos(-1)=\dfrac{\pi}{2}+(\pi -arccos1)=\dfrac{\pi}{2}+\pi -0=\dfrac{3\pi }{2}\\\\6)\ \ arccos\Big(-\dfrac{\sqrt2}{2}\Big)-arccos\dfrac{\sqrt2}{2}=\Big(\pi -arccos\dfrac{\sqrt2}{2}\Big)-\dfrac{\pi}{4}=\pi -\dfrac{\pi}{4}-\dfrac{\pi }{4}=\dfrac{\pi }{2}$