Question

Show cos 20 * cos 40 * cos 80 =1/8

Answer 1

cos 20 cos 40 cos 80 =
= ( 2 sin 20 cos 20 cos 40 cos 80 ) / 2 sin 20 =
( multiple and divide by 2 sin 20 )
= ( sin 40 cos 40 cos 80 ) / 2 sin 20 =
= ( 1/2 sin 80 cos 80 ) / 2 sin 20 =
= ( sin 80 cos 80 ) / 4 sin 20 =
= 1/2 sin 160 / 4 sin 20 =
= sin 160 / 8 sin 20 = ( and since: sin 160 = sin 20 )
= 1 / 8