一道外文题
In a circle we enscribe a regular 2001-gon and inside it a regular 667-gon with shared vertices.Prove that the surface in the 2001-gon but not in the 667-gon is of the form\( k\*\sin^3\left(\frac{\pi}{2001}\right)*\cos^3\left(\frac{\pi}{2001}\right) \)with \( k \) a positive integer. Find \( k \). 这个很好计算了:
\(s= 667*(1/2R^2)*\Big(3\sin(a)-\sin(3a)\Big)= 2*667*R^2*\sin^3(a) .\)
而 \(2001a=2\pi\)
所以, \(k=8\*667 =5336\)
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