Question

помогите решить уравнения
arcsin(-1/2)+arcsin1
2 arccos √3/2 - arctg √3
arccos1-arcsin(-√3/2)
arccos(√2/2)+2arcsin1/2

Answer 1

$1)arcSin(-\frac{1}{2})+arcSin1=-\frac{\pi }{6} +\frac{\pi }{2}=-\frac{\pi }{6}+\frac{3\pi }{6}=\frac{2\pi }{6}=\frac{\pi }{3}\\\\2)2arcCos\frac{\sqrt{3}}{2}-arctg\sqrt{3}=2*\frac{\pi }{6}-\frac{\pi }{3}=\frac{\pi }{3}-\frac{\pi }{3}=0\\\\3)arcCos1-arcSin(-\frac{\sqrt{3}}{2}=0-(-\frac{\pi }{3} )=\frac{\pi }{3}\\\\4)arcCos(\frac{\sqrt{2}}{2}+2arcSin\frac{1}{2}=\frac{\pi }{4}+2*\frac{\pi }{6}=\frac{\pi }{4}+\frac{\pi }{3} =\frac{3\pi+4\pi}{12}=\frac{7\pi}{12}$