MathDB

3

Part of 2001 Flanders Math Olympiad

Problems(1)

Weird trig

Source: flanders '01

8/30/2004
In a circle we enscribe a regular 20012001-gon and inside it a regular 667667-gon with shared vertices. Prove that the surface in the 20012001-gon but not in the 667667-gon is of the form k.sin3(π2001).cos3(π2001)k.sin^3\left(\frac{\pi}{2001}\right).cos^3\left(\frac{\pi}{2001}\right) with kk a positive integer. Find kk.
trigonometrygeometrygeometry proposed