解
y=1/2cos²x+√3/2sinxcosx+1
=1/4(2cos²x-1)+√3/4(2sinxcosx)+5/4
=1/4cos2x+√3/4sin2x+5/4
=1/2[1/2cos2x+√3/2sin2x]+5/4
=1/2[sin2xcosπ/6+cos2xsinπ/6]+5/4
=1/2sin(2x+π/6)+5/4
当2x+π/6=π/2+2kπ
即x=π/6+kπ时
y取得最大值为:1/2+5/4=7/4
∴x的集合为:{x=π/6+kπ,k∈z}
解
y=1/2cos²x+√3/2sinxcosx+1
=1/4(2cos²x-1)+√3/4(2sinxcosx)+5/4
=1/4cos2x+√3/4sin2x+5/4
=1/2[1/2cos2x+√3/2sin2x]+5/4
=1/2[sin2xcosπ/6+cos2xsinπ/6]+5/4
=1/2sin(2x+π/6)+5/4
当2x+π/6=π/2+2kπ
即x=π/6+kπ时
y取得最大值为:1/2+5/4=7/4
∴x的集合为:{x=π/6+kπ,k∈z}