Question

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 1 (b) `-1` (c) 0 (d) none of these

Answer 1

`=(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`.