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Soros Olympiad in Mathematics
II Soros Olympiad 1995 - 96 (Russia)
11.3
3x3 system sin \pi}/ 2 xy =z (II Soros Olympiad 1997-98 R3 11.3)
3x3 system sin \pi}/ 2 xy =z (II Soros Olympiad 1997-98 R3 11.3)
Source:
June 6, 2024
algebra
system of equations
trigonometry
Problem Statement
Solve the system of equations
{
sin
π
2
x
y
=
z
sin
π
2
y
z
=
x
sin
π
2
z
x
=
y
?
\begin{cases} \sin \frac{\pi}{2}xy =z \\ \sin \frac{\pi}{2}yz =x \\ \sin \frac{\pi}{2}zx =y \end{cases} \,\,\, ?
⎩
⎨
⎧
sin
2
π
x
y
=
z
sin
2
π
yz
=
x
sin
2
π
z
x
=
y
?
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