Home Competitions USAMO 1980 Problem 3
A + B + C +B+C + B + C π . x , y , z \pi . x, y, z π . x , y , z x sin A + y sin B + z sin C = x 2 sin 2 A + x \sin A+y \sin B+z \sin C=x^{2} \sin 2 A+ x sin A + y sin B + z sin C = x 2 sin 2 A + y 2 sin 2 B + z 2 sin 2 C = 0 y^{2} \sin 2 B+z^{2} \sin 2 C=0 y 2 sin 2 B + z 2 sin 2 C = 0 x n sin n A + y n sin n B + z n sin n C = 0 x^{n} \sin n A+y^{n} \sin n B+z^{n} \sin n C=0 x n sin n A + y n sin n B + z n sin n C = 0 n n n
Dataset text NuminaMath olympiads . Quoted with source.
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