Question

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

Answer 1

Correct Answer - 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`