求sin12*sin24*sin48*sin96=?

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*sin24*sin48*sin96
=（sin96*sin24）（sin48*sin12）
= -1/2[cos120-cos72]*(-1/2)[cos60-cos36]
= 1/4(-1/2-cos72)(1/2-cos36)
= 1/4(cos72+1/2)(cos36-1/2)
= 1/4cos72cos36+1/8(cos36...