Difference between revisions of "1980 USAMO Problems/Problem 3"
(Created page with "== Problem == <math>A + B + C</math> is an integral multiple of <math>\pi</math>. <math>x, y, </math> and <math>z</math> are real numbers. If <math>x\sin(A)\plus{}y\sin(B)\plus{}...") |
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== See Also == | == See Also == | ||
{{USAMO box|year=1980|num-b=2|num-a=4}} | {{USAMO box|year=1980|num-b=2|num-a=4}} | ||
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[[Category:Olympiad Trigonometry Problems]] | [[Category:Olympiad Trigonometry Problems]] | ||
Revision as of 18:10, 3 July 2013
Problem
is an integral multiple of 
. 
and 
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 
for any positive integer 
.
Solution
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See Also
| 1980 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
