Theorem 5.4c: The area of the region in the figure above is
2r2cos2(180k/n)sin2(180/n)sec(180j/n)tan(180(j-1)/n)sec(180(j-2)/n)
proof2: From Corollary
5.1b we know that the area is
sjsj-1sin(360(j-1)/n). As in the
previous proof,
sjsj-1sin(360(j-1)/n) =
2r2cos2(180k/n)sin2(180/n)sec(180j/n)sec2(180(j-1)/n)
sin(180(j-1)/n)cos(180(j-1)/n)sec(180(j-2)/n)
= 2
r2cos2(180k/n)sin2(180/n)
tan(180(j-1)/n)sec(180j/n)sec(180(j-2)/n)
proof 1
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