求y=(2cosx-m)^2+(sinx)^2的最小值(|m|小于等于2)

y=4(cosx)^2-4mcosx+m^2+(sinx)^2
=3(cosx)^2-4mcosx+m^2+(sinx)^2+(cosx)^2
=3(cosx)^2-4mcosx+m^2+1
=3(cosx-2m/3)^2-4m^2/3+m^2+1
=3(cosx-2m/3)^2-m^2/3+1
开口向上，对称轴cosx=2/3m

|m|<=2
-2<=m<=2
-4/3<=2m/3<=4/3

-1<=cosx<=1

所以
若-4/3<=2m/3<-1,-2<=m<-3/2
则对称轴在定义域左边，y是增函数，所以cosx=-1，y最小=m^2+4m+4
若-1<=2m/3<=1,-3/2<=m<=3/2,则对称轴在定义域内
所以cosx=2m/3,y最小=-m^2/3+1
若1<2m/3<=4/3,3/2<m<=2
则对称轴在定义域右边，y是减函数，所以cosx=1，y最小=m^2-4m+4

综上
-2<=m<-3/2，y最小=m^2+4m+4
-3/2<=m<=3/2,y最小=-m^2/3+1
3/2<m<=2,y最小=m^2-4m+4

y=(2cosx-m)^2+(sinx)^2=4（cosx）^2-4mcosx+1-（cosx）^2=3（cosx）^2-4mcosx+1=3(cosx+2m/3)^2+1-4m^2/3
-4/3≤-2m/3＜－1
最小值为4+4m
-1≤-2m/3≤1
最小值为1-4m^2/3
1＜-2m/3＜4/3
最小值为4-4m

y=3cos^2x-4mcosx+m^2+1
=3(cosx-2m/3)^2+1-m^2/3
由│m│≤2及│2m/3│>1,有
①当-2≤m<-3/2时,
cosx=-1,y最小=