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EGMO TST - Moldova
2018 Moldova EGMO TST
6
Trigonometry problem
Trigonometry problem
Source: EGMO 2018 Moldova TST
February 11, 2018
trigonometry
Problem Statement
Let
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
, and
x
,
y
∈
x,y \in
x
,
y
∈
(
0
,
π
2
)
\left(0,\frac{\pi}{2}\right)
(
0
,
2
π
)
, and
m
∈
(
2
,
+
∞
)
m \in \left(2,+\infty\right)
m
∈
(
2
,
+
∞
)
such that
tan
x
∗
tan
y
=
m
\tan x * \tan y = m
tan
x
∗
tan
y
=
m
. Find the minimum value of the expression
E
(
x
,
y
)
=
cos
x
+
cos
y
E(x,y) = \cos x + \cos y
E
(
x
,
y
)
=
cos
x
+
cos
y
.
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