Question

корень из 2-2cos（5x-пи/3）＝0

Answer 1

$\sqrt{2}-2cos(5x- \frac{ \pi }{3})=0\\-2cos(5x- \frac{ \pi }{3})=- \sqrt{2}\\cos(5x- \frac{ \pi }{3})= \frac{ \sqrt{2} }{2}\\5x- \frac{ \pi }{3}=бarccos\frac{ \sqrt{2} }{2}+2 \pi n, n\in Z\\5x- \frac{ \pi }{3}=б \frac{ \pi }{4}+2 \pi n, n\in Z\\5x=б \frac{ \pi }{4}+ \frac{ \pi }{3}+2 \pi n, n\in Z\\x=б \frac{ \pi }{20}+ \frac{ \pi }{15}+ \frac{2 \pi n}{5}, n\in Z\\\\x_1= \frac{7 \pi }{60}+ \frac{2 \pi n}{5}, n\in Z\\x_2= \frac{ \pi }{60}+ \frac{2 \pi n}{5}, n\in Z$