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pls give a solution for this problem: prove that cos 20.cos 40.cos 60.cos80=1/16

pls give a solution for this problem:
prove that cos 20.cos 40.cos 60.cos80=1/16

Grade:12

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
Dear student,

cos 20`cos 40`cos 60`cos 80` *(8sin 20`/8 sin20`)
=[4 (2 sin 20`cos 20`)cos 40`cos 60`cos 80`]/8 sin20`
= [2 (2 sin 40`cos 40`)cos 60`cos 80`]/8 sin20`
=[(2 sin 80`cos 80`)cos 60`]/8 sin20`
= [(sin 160) (1/2)]/8 sin20` = (1/2)/8 = 1/16

sin 2a = 2 sin a cos a , sin (180 - a) = sin a

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