prove that
cos 20 cos 40 cos 60 cos 80=
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Answer:
cos 20 cos 40 cos 60 cos 80
(1/2)*(2cos20 cos80) cos40 cos60
(1/2)*(cos 100 + cos 60) cos40 cos60
(1/2)*(cos100 + 1/2) cos40 cos60
(1/4)*(2cos100 + 1) cos40* (1/2)
(1/8)*(2cos 100 + 1) cos40
(1/8)*(2cos100 cos40 + cos40)
(1/8)*(cos140 + cos60 + cos40)
(1/8)*( cos (180-40) + cos 60 + cos 40)
(1/8)*( - cos 40 + cos 60 + cos 40)
(1/8)* cos60
(1/8)*(1/2)
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proved
(note: I made group of cos20 cos80 at first, but it is not that the problem will be solved this way only, you can take any other group leaving cos 60 and the problem will be solved. At last you will have to make angle substitution once.)
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