prove that :-cos40 cos80 cos160=-1/8
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sin20.sin40.cos60.cos80 = (1/2)[2 sin20.sin40.cos60.cos80]
= (1/2){[cos 20 + cos 60]cos60.cos80}
= (1/2){[cos 20 + (1/2)](1/2).cos80}
= (1/8){[2cos 20 + 1].cos80}
= (1/8)[2cos 20 cos80 + cos80]
= (1/8)[cos 100 + cos60 + cos80]
= (1/8)[- cos 80 + (1/2) + cos80]
= (1/8) (1/2) = (1/16)
= RHS
= (1/2){[cos 20 + cos 60]cos60.cos80}
= (1/2){[cos 20 + (1/2)](1/2).cos80}
= (1/8){[2cos 20 + 1].cos80}
= (1/8)[2cos 20 cos80 + cos80]
= (1/8)[cos 100 + cos60 + cos80]
= (1/8)[- cos 80 + (1/2) + cos80]
= (1/8) (1/2) = (1/16)
= RHS
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