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

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Show that cos 20 * cos 40 * cos 80 =1/8
asked May 27, 2013 in TRIGONOMETRY by andrew Scholar

1 Answer

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cos 20  cos 40  cos 80   =  1/ 8

cos 20 cos 40  cos 80  =  2 sin 20  cos 20 cos 40 cos 80 /  2 sin 20     ( Multiplying  numerator & denomirator with 2sin 20)

                                      = sin 2 (20)  cos 40  cos 80 / 2 sin 20            (  2 sin a cos a  =  sin 2 a  )

                                     = sin 40 cos 40 cos 80 /  2 sin 20

                                    =  2 sin 40 cos 40  cos 80 / 2 . 2 sin 20     (  Multiplying  numerator & denomirator  with ' 2 ' )

                                    =  sin 2 ( 40 )  cos 80 /  4 sin 20               (  2 sin a cos a  =  sin 2a )

                                   =  2 . sin 80 cos 80  / 2 . 4 sin 20              ( Multiplying  numerator &  denomirator with ' 2 ' )

                                   =  sin 2 ( 80 ) / 8 sin 20                             (  2 sin a cos a  = sin 2a )

                                   =  sin ( 160 ) / 8 sin 20

                                   =  sin ( 180 - 20 ) /  8 sin 20

                                   =  sin 20 / 8 sin 20

                                   =  1/ 8

Therefore  cos 20 cos 40 cos 80  =  1/8.                        

answered Jun 11, 2013 by goushi Pupil

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