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Problems
Contests
National and Regional Contests
Singapore Contests
Singapore MO Open
2008 Singapore MO Open
4
SMO 2008 q4
SMO 2008 q4
Source: SMO 2008
March 30, 2018
inequalities
Problem Statement
let
0
<
a
,
b
<
π
/
2
0<a,b<\pi/2
0
<
a
,
b
<
π
/2
. Show that
5
c
o
s
2
(
a
)
+
5
s
i
n
2
(
a
)
s
i
n
2
(
b
)
c
o
s
2
(
b
)
≥
27
c
o
s
(
a
)
+
36
s
i
n
(
a
)
\frac{5}{cos^2(a)}+\frac{5}{sin^2(a)sin^2(b)cos^2(b)} \geq 27cos(a)+36sin(a)
co
s
2
(
a
)
5
+
s
i
n
2
(
a
)
s
i
n
2
(
b
)
co
s
2
(
b
)
5
≥
27
cos
(
a
)
+
36
s
in
(
a
)
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