1980 USAMO Problems/Problem 3

Problem

$A + B + C$ is an integral multiple of $\pi$ . $x, y,$ and $z$ are real numbers. If $x\sin(A)\plus{}y\sin(B)\plus{}z\sin(C)\equal{}x^2\sin(2A)+y^2\sin(2B)+z^2\sin(2C)=0$ (Error compiling LaTeX. Unknown error_msg), show that $x^n\sin(na)+y^n \sin(nb) +z^n \sin(nc)=0$ for any positive integer $n$ .

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1980 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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1980 USAMO Problems/Problem 3

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