【题目应为：y=根号3 cos（3π/2 +2X）+ cos^2 X -sin^2 X】
y=根号3 cos（3π/2 +2X）+ cos^2 X -sin^2 X
= 根号3 cos {2π-（π/2-2x)} + {cos^2 X -sin^2 X}
= 根号3 cos (π/2-2x) + cos2X
= 根号3 sin2x + cos2x
= 2 ( sin2xcosπ/6 + cos2xsinπ/6)
= 2 sin(2x+π/6)
周期 T = 2π/2 = π
当2x+π/6=2kπ+π/2,即x=kπ+π/6,其中k∈Z时,有最大值ymax=2
当2x+π/6=2kπ-π/2,即x=kπ-π/3,其中k∈Z时,有最小值ymin=-2