若x+y=π/3,則sinx*siny的最小值為A-1 B-0.5 C-0.75 D0.25答案為C,怎么算？

熱心網(wǎng)友

解:x+y=π/3,積化和差sinx*siny=(-1/2)[cos(x+y)+cos(x-y)]=(-1/2)[cos丌/3+cos(x-y)]=(-1/2)[(1/2)+cos(x-y)]=-1/4-(1/2)cos(x-y)≥-1/4-1/2=-3/4=-0.75選C