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Germany Contests
German National Olympiad
1969 German National Olympiad
5
sin 5x = 16 sin x sin (x -\pi/5) sin (x +\pi/5) sin (x -2\pi/5) sin (x +2\pi/5)
sin 5x = 16 sin x sin (x -\pi/5) sin (x +\pi/5) sin (x -2\pi/5) sin (x +2\pi/5)
Source: 1968-69 Germany R4 12.5
October 13, 2024
trigonometry
algebra
Problem Statement
Prove that for all real numbers
x
x
x
holds:
sin
5
x
=
16
sin
x
⋅
sin
(
x
−
π
5
)
⋅
sin
(
x
−
2
π
5
)
sin
(
x
+
2
π
5
)
\sin 5x = 16 \sin x \cdot \sin \left(x -\frac{\pi}{5} \right) \cdot \sin\left(x -\frac{2\pi}{5} \right) \sin \left(x +\frac{2\pi}{5} \right)
sin
5
x
=
16
sin
x
⋅
sin
(
x
−
5
π
)
⋅
sin
(
x
−
5
2
π
)
sin
(
x
+
5
2
π
)
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