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Easy Trigonometric Identity - ILL 1970 - Problem 14.
Easy Trigonometric Identity - ILL 1970 - Problem 14.
Source:
May 24, 2011
trigonometry
Problem Statement
Let
α
+
β
+
γ
=
π
\alpha + \beta +\gamma = \pi
α
+
β
+
γ
=
π
. Prove that
∑
c
y
c
sin
2
α
=
2
⋅
(
∑
c
y
c
sin
α
)
⋅
(
∑
c
y
c
cos
α
)
−
2
∑
c
y
c
sin
α
\sum_{cyc}{\sin 2\alpha} = 2\cdot \left(\sum_{cyc}{\sin \alpha}\right)\cdot\left(\sum_{cyc}{\cos \alpha}\right)- 2\sum_{cyc}{\sin \alpha}
∑
cyc
sin
2
α
=
2
⋅
(
∑
cyc
sin
α
)
⋅
(
∑
cyc
cos
α
)
−
2
∑
cyc
sin
α
.
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