Question

cos 8Пx/6=корень из 3 /2.

Answer 1

$displaystyle cos( frac{8 pi x}{6})= frac{ sqrt{3}}{2}\\cos( frac{4 pi x}{3})= frac{ sqrt{3}}{2}\\ left { {{ frac{4 pi x}{3}= frac{ pi }{6}+2 pi n} atop { frac{4 pi x}{3}=- frac{ pi }{6}+2 neq n}} right.\\ left { {{x= frac{ pi }{6}* frac{3}{4 pi }+2 pi n* frac{3}{4 pi }} atop {x=- frac{ pi }{6}* frac{3}{4 pi }+2 pi n* frac{3}{4 pi }}} right.\\ left { {{x= frac{1}{8}+ frac{3}{2}n} atop {x=- frac{1}{8}+ frac{3}{2}n}} right. \\nin Z$