Question

$2cos7xcdot cos(-x)+cos10x=0$

 

Answer 1

cos(7x-x)+cos(7x+x)+cos10x=cos10x+cos6x+cos8x=2cos8xcos2x+cos8x=

cos8x(2cos2x+1)=0

cos8x=0  8x=П(2k+1)  x=П(2k+1)/8

cos2x=-1/2

2x=(П+-П/3)+2Пk

x=(П/2+-П/6)+Пk

ответ

x=П/3+пk

x=2П/3+Пk

x=П(2k+1)/8