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2016 Moldova Team Selection Test
9
you wouldn't believe this is from TST if I didn't tell you
you wouldn't believe this is from TST if I didn't tell you
Source: MDA TST 2016, 9
March 26, 2019
algebra
Problem Statement
Let
α
∈
(
0
,
π
2
)
\alpha \in \left( 0, \dfrac{\pi}{2}\right)
α
∈
(
0
,
2
π
)
.Find the minimum value of the expression
P
=
(
1
+
cos
α
)
(
1
+
1
sin
α
)
+
(
1
+
sin
α
)
(
1
+
1
cos
α
)
.
P = (1+\cos\alpha)\left(1+\frac{1}{\sin \alpha} \right)+(1+\sin \alpha)\left(1+\frac{1}{\cos \alpha} \right) .
P
=
(
1
+
cos
α
)
(
1
+
sin
α
1
)
+
(
1
+
sin
α
)
(
1
+
cos
α
1
)
.
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