cos 2π/7 +cos 4π/7 +cos 6π/7=?

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cos 2π/7 +cos 4π/7 +cos 6π/7=?

原式
=2sin(π/7)[cos(2π/7)+cos(4π/7)+cos(6π/7)]/2sin(π/7)
=[2sin(π/7)cos(2π/7)+2sin(π/7)cos(4π/7)+2sin(π/7)cos(6π/7)]/2sin(π/7)
=[sin(3π/7)-sin(π/7)+sin(5π/7)-sin(3/7)+sin(7π/7)-sin(5π/7)]/2sin(π/7)
=[sin(7π/7)-sin(π/7)]/2sin(π/7)
=-sin(π/7)/2sin(π/7)
=-1/2.