4sinxsin2xTncos2(n-1)α={-cos3x+cos(2n-3)x+cos(2n-1)x-cos(4n-1)x}

4sinxsin2xTnsin2(n-1)α={sin3x+sin(2n-3)x+sin(2n-1)x-sin(4n-1)x}

4sinxsin2xΣTncos2(n-1)α={-Σcos3x+Σcos(2n-3)x+Σcos(2n-1)x-Σcos(4n-1)x}

4sinxsin2xΣTnsin2(n-1)α={Σsin3x+Σsin(2n-3)x+Σsin(2n-1)x-Σsin(4n-1)x}

{-Σcos3x+Σcos(2n-3)x+Σcos(2n-1)x-Σcos(4n-1)x}^2+{Σsin3x+Σsin(2n-3)x+Σsin(2n-1)x-Σsin(4n-1)x}^2

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合わせると

n^2

2{sin(nx)/sin(x)}^2

{sin(2nx)/sin(2x)}^2

-2ncos(n+1)xsin(nx)/sin(x)

-2ncos(n+3)xsin(nx)/sin(x)

2ncos(2n+4)xsin(2nx)/sin(2x)

2{sin(nx)/sin(x)}^2・cos2x

-2cos((n+3)x)・sin(nx)/sin(x)・sin(2nx)/sin(2x)

-2cos((n+1)x)・sin(nx)/sin(x)・sin(2nx)/sin(2x)

ここまでは数値的にも合致していることを確認した。

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