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The value of cospi/7+cos(2pi)/7+cos(3pi)...

The value of `cospi/7+cos(2pi)/7+cos(3pi)/7+cos(4pi)/7+cos(5pi)/7+cos(6pi)/7+cos(7pi)/7` is 1 (b) `-1` (c) 0 (d) none of these

A

1

B

-1

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`cos.pi/7+cos.(2pi)/7+cos.(3pi)/7+cos.(4pi)/7+cos.(5pi)/7+cos.(6pi)/7+cos.(7pi)/7`
`=(cos.pi/7+cos.(6pi)/7)+(cos.(2pi)/7+cos.(5pi)/7)+(cos.(3pi)/7+cos.(4pi)/7)+cospi`
`=(cos.pi/7-cos.pi/7)+(cos.(2pi)/7-cos.(2pi)/7)+(cos.(3pi)/7-cos.(3pi)/7)+cospi`
`=cospi=-1`
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