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Find the value of cos(2pi)/7+cos(4pi)/7+...

Find the value of `cos(2pi)/7+cos(4pi)/7+cos(6pi)/7`

Text Solution

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`S=cos""(2pi)/(7)+ cos ""( 4pi)/(7) +cos""(6pi)/(7)`
`(sin""(3(pi)/(7)))/(sin""((pi)/(7)))cos""((pi)/(7)+(3pi)/(7))=(2sin((3pi)/(7))cos((4pi)/(7)))/(2sin((pi)/(7)))`
`=(sin((7pi)/(7))-sin((pi)/(7)))/(2sin((pi)/(7)))=-(1)/(2)`
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