f(x)=5sinxcosx-5根号3(cosx)^2+5根号3/2=5/2[2sinxcosx-(根号3×2(cosx)^2-根号3)]=5/2(sin2x-根号3cos2x)=5sin(2x-π/3)-π/2+2kπ<2x-π/3<π/2+2kπ π/12+kπx=5π/12+kπ时有最大值
