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

Multiply top and bottom by 2 sin 20
cos 20.cos 40.cos 80 = 2 sin 20 cos 20.cos 40.cos 80 / 2 sin 20
ie, sin 40 cos 40 cos 80 / 2 sin 20 then multiply top and bottom by 2 ,
 2 sin 40 cos 40 cos 80 / 4 sin 20
ie, sin 80 cos 80/ 4 sin 20 and by 2 again
 2 sin 80 cos 80 /8 sin 20
 => sin 160 / 8 sin 20
=> sin ( 180 -20) / 8 sin 20
=> sin 20/8 sin 20 = 1/8


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