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China Contests
China Northern MO
2011 China Northern MO
7
2011-china-northern-mathematical-olympiad, p7
2011-china-northern-mathematical-olympiad, p7
Source:
September 29, 2011
trigonometry
inequalities
inequalities unsolved
China
Problem Statement
In
△
A
B
C
\triangle ABC
△
A
BC
, then
1
1
+
cos
2
A
+
cos
2
B
+
1
1
+
cos
2
B
+
cos
2
C
+
1
1
+
cos
2
C
+
cos
2
A
≤
2
\frac{1}{1+\cos^2 A+\cos^2 B}+\frac{1}{1+\cos^2 B+\cos^2 C}+\frac{1}{1+\cos^2 C+\cos^2 A}\le 2
1
+
cos
2
A
+
cos
2
B
1
+
1
+
cos
2
B
+
cos
2
C
1
+
1
+
cos
2
C
+
cos
2
A
1
≤
2
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