cosX+cos2X=0
cosx+2(cosx)^2-1=0
2(cosx)^2+cosx-1=0
(cosx+1)(2cosx-1)=0
cosx=-1或cosx=1/2
x=π+2kπ或-π+2kπ
或x=π/3+2kπ或-π/3+2kπ