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sines fraction and cosines fraction

Source: IMO Longlist 1967, Poland 5

October 14, 2005
trigonometryLaTeXgeometry unsolvedgeometry

Problem Statement

Show that the triangle whose angles satisfy the equality sin2(A)+sin2(B)+sin2(C)cos2(A)+cos2(B)+cos2(C)=2 \frac{sin^2(A) + sin^2(B) + sin^2(C)}{cos^2(A) + cos^2(B) + cos^2(C)} = 2 is a rectangular triangle.
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