■正多角形の高さ(その3)

[5]正七角形

a=2sin180/7

b=2sin180/7・3

c=2sin180/7・2

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sin180/7=sinx=y

a^2+b^2+c^2=4((sinx)^2+(2sinxcosx)^2+(-4sinx^3+3sinx)^2)

=4(y^2+4y^2(1-y^2)+16y^6-24y^4+9y^2)

=4(16y^6-28y^4+14y^2)

sin7x=-64y^7+112y^5-56y^3+7y=-y(64y^6-112y^4+56y^2-7)=0

したがって、64y^6-112y^4+56y^2=7

a^2+b^2+c^2=7

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