ｎを奇数とする

目標とする交点の座標は(1/2,1/2tanα)である。

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nn=n+1,α=π/nn

y=(sin((nn-2)π/nn)) /(cos((nn-2)π/nn)-1)・(x-1)

y-sin(2π/nn)=(sin((nn+4)π/nn)-sin(2π/nn)) /(cos((nn+4)π/nn)-cos(2π/nn))・(x-cos(2π/nn))

y=(sin(2π/nn)) /(-cos((2π/nn)-1)・(x-1)

y-sin(2π/nn)=(-sin(4π/nn)-sin(2π/nn)) /(-cos(4π/nn)-cos(2π/nn))・(x-cos(2π/nn))

y=(sin(2α)) /(-cos2α-1)・(x-1)

y-sin2α=(-sin4α-sin2α) /(-cos4α-cos2α)・(x-cos2α)

交点は

(sin(2α)) /(-cos2α-1)・(x-1)=(sin4α+sin2α) /(cos4α+cos2α)・(x-cos2α)+sin2α

(+cos4α+cos2α)(sin(2α)) ・(x-1)=(-cos2α-1)(sin4α+sin2α) ・(x-cos2α)+(-cos2α-1)sin2α(cos4α+cos2α)

(2cos2α-1)(cos2α+1)(sin(2α)) ・(x-1)=(-cos2α-1)sin2α (2cos2α+1) ・(x-cos2α)-(cos2α+1)sin2α(cos4α+cos2α)

(2cos2α-1)・(x-1)=-(2cos2α+1) ・(x-cos2α)-(cos4α+cos2α)

4cos2α・x=(2cos2α-1)+ cos2α(2cos2α+1)-(cos4α+cos2α)

4cos2α・x=2(cos2α)^2+3cos2α-(cos4α+cos2α)-1=2cos2α

x=1/2

y=(sin(2α)) /(cos2α+1)・1/2=1/2・tanα

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