sinx*siny=[cos(x-y)-cos(x+y)]/2=[cos(x-y)-1/2]/2=1/2cos(x-y)-1/4-1/2≤1/2cos(x-y)≤1/2-3/4≤1/2cos(x-y)-1/4≤1/4-3/4≤sinxsiny≤1/4当x=120°,y=-60°时 sinxsiny=-3/4 达到最小值故（sinxsiny)min=-3/4....