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Moldova Contests
Moldova National Olympiad
2009 Moldova National Olympiad
12.3
12.3
Part of
2009 Moldova National Olympiad
Problems
(1)
Trigonometric equation
Source: Moldova national olympiad 2009
10/5/2015
Find all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of real numbers, so that
sin
(
2009
x
)
+
sin
(
a
x
)
+
sin
(
b
x
)
=
0
\sin(2009x)+\sin(ax)+\sin(bx)=0
sin
(
2009
x
)
+
sin
(
a
x
)
+
sin
(
b
x
)
=
0
holds for any
x
∈
R
x\in \mathbf {R}
x
∈
R
.
trigonometry
algebra
equation
Trigonometric Equations