MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1980 All Soviet Union Mathematical Olympiad
292
ASU 292 All Soviet Union MO 1980 trigonometric system of equation
ASU 292 All Soviet Union MO 1980 trigonometric system of equation
Source:
July 19, 2019
trigonometry
system of equations
algebra
Problem Statement
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
Back to Problems
View on AoPS