Question

cos5x+cosx=0решите плиз поскорее. Срочно

Answer 1

$cos5x+cosx=0 \\\ 2cos\frac{5x+x}{2}cos\frac{5x-x}{2}=0 \\\ cos3xcos2x=0 \\\ cos3x=0 \\\ 3x=\frac{\pi}{2}+\pi n \\\ x=\frac{\pi}{6}+\frac{\pi n}{3}, n\in Z \\\ cos2x=0 \\\ 2x=\frac{\pi}{2}+\pi n \\\ x=\frac{\pi}{4}+\frac{\pi n}{2}, n\in Z$

Ответ: $x=\frac{\pi}{6}+\frac{\pi n}{3}, n\in Z$ и $x=\frac{\pi}{4}+\frac{\pi n}{2}, n\in Z$