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The value of cos(pi/7)+cos((2pi)/7)+cos(...

The value of `cos(pi/7)+cos((2pi)/7)+cos((3pi)/7)+cos((4pi)/7)+cos((5pi)/7)` `+cos((6pi)/7)+cos((7pi)/7)` is

A

1

B

-1

C

0

D

none of these

Text Solution

Verified by Experts

`=(cos(pi/7)+cos(6/7pi))+(cos(2/7pi)+cos(5/7pi))+(cos(3/7pi)+cos(4/7pi))+cospi`
`=2cos(pi/2)cos(-5/14pi)+2cos(pi/2)*cos(-3/14pi)+2cos(pi/2)cos(-pi/14)+(-1)`
`=0+0+0-1`
`=-1`.
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