1980 USAMO Problems/Problem 3

Problem

$A + B + C$ is an integral multiple of $\pi$ . $x, y,$ and $z$ are real numbers. If $x\sin(A)+y\sin(B)+z\sin(C)=x^2\sin(2A)+y^2\sin(2B)+z^2\sin(2C)=0$ , show that $x^n\sin(nA)+y^n \sin(nB) +z^n \sin(nC)=0$ for any positive integer $n$ .

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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

Page

Toolbox

Search

1980 USAMO Problems/Problem 3

Problem

Solution

See Also