f（x）=cos（π-x）sin（π/2+x）+根号3sinxcosx.求当x属于【0,π/2】是f（x）的最大值和最小值

题目

f（x）=cos（π-x）sin（π/2+x）+根号3sinxcosx.求当x属于【0,π/2】是f（x）的最大值和最小值

答案

f(x)=cos(π-x)sin(π/2-x)+√3sinxcosx
=-(cosx)^2+(√3/2)sin2x
=(√3/2)sin2x-(1/2)cos2x-1/2
=sin2xcosπ/6-cos2xsinπ/6-1/2
=sin(2x-π/6)-1/2
0