Published by admin on September 15, 2020 ##cos(2pi/5)=(-1+sqrt(5))/4## Here the most elegant solution I found in: http://math.stackexchange.com/questions/7695/how-to-prove-cos-frac2-pi-5-frac-1-sqrt54 ##cos(4pi/5)=cos(2pi-4pi/5)=cos(6pi/5)## So if ## x=2pi/5##: ##cos(2x)=cos(3x)## Replacing the cos(2x) and cos(3x) by their general formulae: ##color(red)(cos(2x)=2cos^2x-1 […]