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Canadian Mathematical Olympiad Qualification Repechage
2021 Canadian Mathematical Olympiad Qualification
7
Symmetrical three variable cosine equation
Symmetrical three variable cosine equation
Source: Canada Repêchage 2021/7 CMOQR
March 30, 2021
Canada
repechage
algebra
trigonometry
Problem Statement
If
A
,
B
A, B
A
,
B
and
C
C
C
are real angles such that
cos
(
B
−
C
)
+
cos
(
C
−
A
)
+
cos
(
A
−
B
)
=
−
3
/
2
,
\cos (B-C)+\cos (C-A)+\cos (A-B)=-3/2,
cos
(
B
−
C
)
+
cos
(
C
−
A
)
+
cos
(
A
−
B
)
=
−
3/2
,
find
cos
(
A
)
+
cos
(
B
)
+
cos
(
C
)
\cos (A)+\cos (B)+\cos (C)
cos
(
A
)
+
cos
(
B
)
+
cos
(
C
)
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