题目内容：

已知函数f(x)=sinxcosx-根号下3sin2x（2是sinx的平方的意思）
1、求f(x)的最小正周期
2、求f(x)在区间【0,π/2】上的最大值和最小值.

优质解答

f(x) = 1/2 sin2x - √3 /2 (1 - cos2x )
= 1/2 sin2x + √3/2 cos2x - √3/2
= sin(2x+ π/3) - √3/2
1、最小正周期 T = 2π/2 = π
2、0 ≤ x ≤ π/2
π/3 ≤ 2x +π/3 ≤ 4π/3
当 2x+π/3 = 4π/3 时取最小值 f(x)min = sin(4π/3) - √3 /2 = - √3
当 2x+π/3 = π/2 时取最大值 f(x)max = sin(π/2) - √3/2 = 1 - √3/2