hitung nilai eksak dari sin 20 sin 40 sin 60 sin 80

sin(20)sin(40) = (1/2)[cos(20) - cos(60)]
=> sin(20)sin(40)sin(80)
= (1/2)[cos(20) - cos(60)]sin(80)
= (1/2)[cos(20)sin(80) - cos(60)sin(80)]
= (1/2)[(1/2)(sin(100)+sin(60)) - (1/2)(sin(140)+sin(20))]
= (1/4)[sin(80) + sin(60) - sin(40) - sin(20)]
= (1/4)sin(60)
= akar(3)/8

NOTE: sin(80) - sin(40) - sin(20) = sin(60+20) - sin(60-20) - sin(20) = 2cos(60)sin(20) - sin(20) = 0