sin12*sin24*sin48*sin84怎么计算不要计算器

Question

sin12*sin24*sin48*sin84怎么计算 不要计算器

Answer 1

sin12*sin24*sin48*sin84
=（sin84*sin24）（sin48*sin12）
= -1/2[cos108-cos60]*(-1/2)[cos60-cos36]
= 1/4(cos108-1/2)(1/2-cos36)
= 1/4(cos72+1/2)(cos36-1/2)
= 1/4cos72cos36+1/8(cos36-cos72)-1/16
= 1/4cos72cos36+1/8*(-2)sin54sin(-18)-1/16
= 1/4cos72cos36+1/4cos36cos72-1/16
=1/2cos36cos72-1/16
=1/4*(2sin36cos36cos72)/sin36-1/16
=1/4*sin72cos72/sin36-1/16
=1/8*sin144/sin36-1/16
=1/8-1/16
=1/16