■フェルマー素数と正十七角形(その35)

[2]式を書くだけでも大変なので,結果だけ書くと=√41-1

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[2]cos2π/41+cos8π/41+cos18π/41-cos9π/41-cos9π/41+cos10π/41+cos16π/41-cos5π/41+cos2π/41-cos5π/41+cos4π/41-cosπ/41+

cos10π/41+cos18π/41-cosπ/41+cos20π/41+cos4π/41+cos8π/41+cos16π/41

+cos20π/41+cos20π/41+cos16π/41+cos8π/41+cos4π/41+

cos20π/41-cosπ/41+cos18π/41+cos10π/41-cosπ/41+cos4π/41-cos5π/41+cos2π/41-cos5π/41+cos16π/41+cos10π/41-cos9π/41+

-cos9π/41+cos18π/41+cos8π/41+cos2π/41=

-4cos(π/41)+4cos(2π/41)+4cos(4π/41)-4cos(5π/41)+4cos(8π/41)-4cos(9π/41)+4cos(10π/41)+4cos(16π/41)+2cos(18π/41)+4cos(20π/41)=√41-1

が得られた.

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