Question

решите уравнение 2cos2x+корень из 2=0​

Answer 1

$2cos2x+\sqrt{2}=0 \\2cos2x=-\sqrt{2}\\cos2x=-\frac{\sqrt{2}}{2}\\2x=+-arccos(-\frac{\sqrt{2}}{2})+2\pi n\\2x=+-(\pi -arccos(\frac{\sqrt{2}}{2})+2\pi n\\2x=+-(\pi -\frac{\pi }{4})+2 \pi n\\2x=+-\frac{3\pi }{4} +2\pi n\\x=+-\frac{3\pi }{8}+\pi n$; n ∈ Z