已知函数f(x)=根号3sinxcosx-(cosx)^2+1/2,求f(x)的最小值及此时x的值

f(x)=（√3）sinxcosx-(cosx）^2+1/2
=[（√3）/2]sin2x-(1+cos2x）/2+1/2
=[（√3）/2]sin2x-(1/2）cos2x
=cos（π/6）sin2x-sin(π/6）cos2x
=sin(2x-π/6)
当2x-π/6=2kπ-π/2,即x=kπ-π/6时,
f(x)=-1为最小值.

由题设得：2f(x)=√3sin2x-cos2x=2sin(2x-π/6).===>f(x)=sin(2x-π/6).易知，当2x-π/6=2kπ-π/2时，即x=kπ-π/6(k为整数）时，f(x)min=-1.