Re: Radical Expression For cos(2*pi/23)

Introduction
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The following approach aims to describe cos(2*pi/p) in terms of cos(4*pi/(p-1)) where p is a prime number.
So, cos(2*pi/23) shall be described in terms of cos(2*pi/11)


Radical Expression For cos(2*pi/23)
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cos(2*pi/23)=(g1+g2+g3+g4+g5+g6+g7+g8+g9+g10-1)/22

where

g1=(k1/2-(k1^2/4-23^11)^(1/2))^(1/11)
g2=(k2/2+(k2^2/4-23^11)^(1/2))^(1/11)*w^8
g3=(k3/2-(k3^2/4-23^11)^(1/2))^(1/11)*w^3
g4=(k4/2+(k4^2/4-23^11)^(1/2))^(1/11)*w^10
g5=(k5/2+(k5^2/4-23^11)^(1/2))^(1/11)*w^2
g6=(k5/2-(k5^2/4-23^11)^(1/2))^(1/11)*w^9
g7=(k4/2-(k4^2/4-23^11)^(1/2))^(1/11)*w
g8=(k3/2+(k3^2/4-23^11)^(1/2))^(1/11)*w^8
g9=(k2/2-(k2^2/4-23^11)^(1/2))^(1/11)*w^3
g10=(k1/2+(k1^2/4-23^11)^(1/2))^(1/11)

w=exp(2*pi*i/11)

k1=46*(e1*cos(2*pi/11) + e2*cos(4*pi/11) + e3*cos(6*pi/11) + e4*cos(8*pi/11) + e5*cos(10*pi/11))
k2=46*(e1*cos(4*pi/11) + e2*cos(8*pi/11) + e3*cos(10*pi/11)+ e4*cos(6*pi/11) + e5*cos(2*pi/11))
k3=46*(e1*cos(6*pi/11) + e2*cos(10*pi/11)+ e3*cos(4*pi/11) + e4*cos(2*pi/11) + e5*cos(8*pi/11))
k4=46*(e1*cos(8*pi/11) + e2*cos(6*pi/11) + e3*cos(2*pi/11) + e4*cos(10*pi/11)+ e5*cos(4*pi/11))
k5=46*(e1*cos(10*pi/11)+ e2*cos(2*pi/11) + e3*cos(8*pi/11) + e4*cos(4*pi/11) + e5*cos(6*pi/11))

e1=-1451316
e2=69291
e3=149151
e4=-486583
e5=-581326
.

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