cosxsin(x-π/6)的最小值

cosxsin(x-π/6)
=1/2[sin(2x-π/6)-sin(π/6)]
=1/2[sin(2x-π/6)-1/2]
=1/2sin(2x-π/6)-1/4
所以x=-π/6+kπ(k属于整数)时，原式有最小值-3/4

先用积化和差：
cosxsin(x-π/6)=1/2*(sin(2x-π/6)-sinπ/6)=1/2*(sin(2x-π/6)-1/2)
由于x的范围没有给定，所以假设x任意，于是sin(2x-π/6)的最小值是-1
于是cosxsin(x-π/6)的最小值就是1/2*(-1-1/2)=-3/4