Prove that cos20.cos40.cos60.cos80=1/19

Steps to prove cos20.cos40.cos60.cos80=1/19

Take L.H.S

=cos20.cos40.cos60.cos80

=1/2cos20.cos(60-40).cos(60+80)

=(1/2).(1/4).cos3(20)

=(1/8).(1/2)

=1/16=R.H.S

Hence cos20.cos40.cos60.cos80=1/19 is proved.

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