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2014-07-28T18:37:16+05:30

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Sin A sin B = 1/2 [ cos A-B  - Cos A+B ]
sin A cos B  = 1/2 [ sin A+B  + sin A-B ]                  also  sin Ф  = sin π - Ф

sin  4π/7  =  sin (π - 4π/7)  = Sin 3π/7

     Sin π/7 Sin 4π/7  =  Sin π/7 Sin 3π/7  =  1/2  [ cos 2π/7  -  cos 4π/7  ]

  Sin π/7 Sin 4π/7  Sin 2π/7    =  1/2  [ Sin 2π/7  Cos 2π/7  -  Sin 2π/7 Cos 4π/7  ]
                   = 1/2 1/2 [ Sin 4π/7 + Sin 0 -   (Sin 6π/7  + Sin -2π/7 ) ] 
                   = 1/4 [ Sin 4π/7 -  sin π/7  + sin 2π/7 ]

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