Hello ,

I wanted to find a relationship between the number of sides of a regular polygon inscribed in a unit circle and the length of side of the polygon (The vertices are roots of equation in the form of Z^n=1).

I came up with two equation that Length = 2sin(pi/n) and Length= Sqrt(2-2cos(2pi/n) , where n is the number of sides.

I was able to prove the two roles geometrically ,

But I need to prove them , or at least one of them analytically (e.g. using algebra)

Can you help me?