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All-Russian Olympiad
1980 All Soviet Union Mathematical Olympiad
292
292
Part of
1980 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 292 All Soviet Union MO 1980 trigonometric system of equation
Source:
7/19/2019
Find real solutions of the system :
{
sin
x
+
2
sin
(
x
+
y
+
z
)
=
0
sin
y
+
3
sin
(
x
+
y
+
z
)
=
0
sin
z
+
4
sin
(
x
+
y
+
z
)
=
0
\begin{cases} \sin x + 2 \sin (x+y+z) = 0 \\ \sin y + 3 \sin (x+y+z) = 0\\ \sin z + 4 \sin (x+y+z) = 0\end{cases}
⎩
⎨
⎧
sin
x
+
2
sin
(
x
+
y
+
z
)
=
0
sin
y
+
3
sin
(
x
+
y
+
z
)
=
0
sin
z
+
4
sin
(
x
+
y
+
z
)
=
0
trigonometry
system of equations
algebra