y=cos2x+8cosx
= 2*(cosx)^2 - 1 + 8cosx
令t = cosx
则有t∈[-1,1]
t = 2t^2 + 8t -1
=2(t+2)^2 -10
对称轴是t=-2
开口向上
那么当t=-1时取最小值y = -8;
当t=1时取最大值=8
所以值域是{y|-8