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South Africa Contests
South Africa National Olympiad
1998 South africa National Olympiad
2
Maximum value
Maximum value
Source: South Africa 1998
September 30, 2005
trigonometry
geometry
perimeter
inequalities
Euler
trig identities
Law of Sines
Problem Statement
Find the maximum value of
sin
2
α
+
sin
2
β
+
sin
2
γ
\sin{2\alpha} + \sin{2\beta} + \sin{2\gamma}
sin
2
α
+
sin
2
β
+
sin
2
γ
where
α
,
β
\alpha,\beta
α
,
β
and
γ
\gamma
γ
are positive and
α
+
β
+
γ
=
18
0
∘
\alpha + \beta + \gamma = 180^{\circ}
α
+
β
+
γ
=
18
0
∘
.
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