Cos(2x+x) + 2cosx=0
cos2x cosx - sin2x sinx +2cosx=0
(cos²x-sin²x)cosx - 2sinx cosx sinx +2cosx=0
(cos²x-sin²x)cosx - 2sin²x cosx + 2cosx=0
cosx (cos²x-sin²x - 2sin²x +2)=0
cosx (cos²x-3sin²x+2)=0
cosx=0 cos²x-3sin²x+2=0
x=π + πn cos²x-3(1-cos²x)+2=0
2 cos²x - 3 +3cos²x+2=0
4cos²x-1=0
(2cosx-1)(2cosx+1)=0
2cosx-1=0 2cosx+1=0
2cosx=1 2cosx=-1
cosx= 1 cosx= -1
2 2
x=+ arccos 1 +2πn x=+ arccos(-1 )+2πn
2 2
x=+ π + 2πn x=+ (π - π)+2πn
3 3
x=+2π +2πn
3
Ответ: х= π +πn
2
x= + π +2πn
3
x=+2π +2πn
3