化简三角函数~!

sin12*sin24*sin48*sin96
=sin12*sin48*sin24*sin96
=1/2(cos36-cos60)*1/2(cos72-cos120)
=1/16(2cos36-1)(2cos72+1)
=1/16(4cos36cos72+2cos36-2cos72-1)
=1/16(4cos36cos72+4sin18sin54-1)
=1/16(4cos36cos72+4cos36cos72-1)
=1/16(8cos36cos72-1)
=1/16(8sin36cos36cos72/sin36-1)
=1/16(4sin72cos72/sin36-1)
=1/16(2sin144/sin144-1)
=1/16(2-1)
=1/16

sin12*sin48=-1/2[cos(12+48)-cos(48-12)]=-1/2[cos60-cos36] ,sin24*sin96 =-1/2[cos(24+96)-cos(96-24)]==-1/2[cos 120-cos 72] 原式=1/4[1/2-cos 36][1/2-cos72]=1/4[-1/4-1/2(cos72-cos36+cos36*cos72)]。又因为cos36*cos72=1/2[cos36+cos72] 原式=1/4[-1/4-1/2(cos72-cos36-cos72-cos36)]=-1/16+1/4cos36