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Prove that cos20cos40cos60cos80=1/16Prove that sin10sin30sin50sin70=1/16
Asked by Gaurav Kudva(student) , on 19/5/12


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  sin10sin30sin50sin70

=  1/2 (sin10sin50sin70)

multiply n divide by 2

 = 1/4 ((2sin10sin50) sin70)

  = 1/4 ((cos(10-50 ) - cos(10 +50)) sin70)

  1/4 ((cos40 - 1/2)sin70)

  = 1/4 cos40 sin70 -  1/8 sin70

  =  1/8 (2 sin70 cos40)  - 1/8 sin70

  =  1/8 ( sin110 + sin30 )  -1/8 sin70

  = 1/8 ( sin(180-70)  +1/2)  -1/8 sin70

  =  1/8 sin70 + 1/16 - 1/8 sin70

  = 1/16

Posted by Ajinder Singhon 19/5/12

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