■正五角形と正十七角形(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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