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prove that : sin 4 180/16 + sin 4 3x180/16 + sin 4 5x180/16 + sin 4 7x180/16 = 3/2 HERE x= multiplication sign , 180 = pie ------------------- Ankit Agrawal

prove that  :


sin4180/16 + sin4 3x180/16 + sin4 5x180/16 + sin7x180/16 = 3/2


HERE x= multiplication sign , 180 = pie 


                        ------------------- Ankit Agrawal

Grade:11

1 Answers

Nikhil Cherukupalli
16 Points
9 years ago

 put sin47x180/16 as sin4(8x180/16- 180/16) = cos4 180/16... Similarly,sin45x180/16 = cos43x180/16..

the lhs can be rearranged to (sin4180/16 + cos4180/16) + (sin43x180/16 + cos43x180/16)

      = 1-2 (sin2180/16)(cos2180/16) + 1- 2 (sin23x180/16)(cos23x180/16)

      = 2- [sin2(2x180/16)]/2 - [sin2(6x180/16)]/2... but sin2(6x180/16) = cos2(2x180/16)

      =>2-[sin2(2x180/16) + cos2(2x180/160]/2 = 2-1/2 = 3/2 = rhs

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