解y=√3cos2x+sin2x+1=2(√3/2cos2x+1/2sin2x)+1=2(sin2xcosπ/3+cos2xsinπ/3)+1=2sin(2x+π/3)+1∵sin(2x+π/3)∈[-1.1]∴当sin(2x+π/3)=1时y取得最大值为：3∴x的集合为：2x+π/3=π/2+2kπ∴x=π/12+kπ...