若x+y=π/3,则sinx*siny的最小值
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sinx*siny=[cos(x-y)-cos(x+y)]/2=[cos(x-y)-1/2]/2=1/2*cos(x-y)-1/4.易知-1≤cos(x-y)≤1,====>-1/2≤1/2*cos(x-y)≤1/2.===>-3/4≤1/2*cos(x-y)-1/4≤1/4.====>-3/4≤sinxsiny≤1/4.易知当x=120°,y=-60°时,sinxsiny=-3/4,达到最小值.故(sinxsiny)min=-3/4.