题目内容：

设函数f(x)=根号3cos^x+sinxcosx-根号3/2
（1）求函数f(x)的最小正周期T,并求出函数f(x)的单调递增区间.
（2）求在[0,3π）内使f(x)取到最大值的所有x的和.

优质解答

解 f(x)=√3cos²x+sinxcosx-√3/2
=√3*(1+cos2x)/2+(1/2)sin2x-√3/2
=(1/2)sin2x+(√3/2)cos2x
=sin(2x+π/3)
∴T=π
单增区间：-π/2+2kπ≤2x+π/3≤π/2+2kπ,k∈Z
-5π/6+2kπ≤2x≤π/6+2kπ,k∈Z
-5π/12+kπ≤x≤π/12+2kπ,k∈Z
即为：[-π/12+kπ,5π/12+kπ],k∈Z
(2)结合图像,5π/12+17π/12+29π/12=51π/12