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Problem
Problem
Find all the numbers '
a
a
a
' for which any root of the equation
sin
3
x
=
a
sin
x
+
(
4
−
2
∣
a
∣
)
sin
2
x
\sin 3x = a \sin x + (4 - 2|a|) \sin^2 x
sin
3
x
=
a
sin
x
+
(
4
−
2∣
a
∣
)
sin
2
x
is a root of the equation
sin
3
x
+
cos
2
x
=
1
+
2
sin
x
cos
2
x
\sin 3x + \cos 2x = 1 + 2 \sin x \cos 2x
sin
3
x
+
cos
2
x
=
1
+
2
sin
x
cos
2
x
and any root of the latter equation is a root of the former.
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