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National and Regional Contests
Vietnam Contests
Vietnam Team Selection Test
2007 Vietnam Team Selection Test
3
Vietnam TST 2007
Vietnam TST 2007
Source:
April 7, 2007
trigonometry
inequalities
search
inequalities proposed
geometry
Problem Statement
Given a triangle
A
B
C
ABC
A
BC
. Find the minimum of
cos
2
A
2
cos
2
B
2
cos
2
C
2
+
cos
2
B
2
cos
2
C
2
cos
2
A
2
+
cos
2
C
2
cos
2
A
2
cos
2
B
2
.
\frac{\cos^{2}\frac{A}{2}\cos^{2}\frac{B}{2}}{\cos^{2}\frac{C}{2}}+\frac{\cos^{2}\frac{B}{2}\cos^{2}\frac{C}{2}}{\cos^{2}\frac{A}{2}}+\frac{\cos^{2}\frac{C}{2}\cos^{2}\frac{A}{2}}{\cos^{2}\frac{B}{2}}.
cos
2
2
C
cos
2
2
A
cos
2
2
B
+
cos
2
2
A
cos
2
2
B
cos
2
2
C
+
cos
2
2
B
cos
2
2
C
cos
2
2
A
.
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