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3
Czech republic,district round,2009,problem 3
Czech republic,district round,2009,problem 3
Source:
February 18, 2012
trigonometry
geometry proposed
geometry
Problem Statement
A
,
B
,
C
A,B,C
A
,
B
,
C
are the three angles in a triangle such that
2
sin
B
sin
(
A
+
B
)
−
cos
A
=
1
2\sin B\sin (A+B)-\cos A=1
2
sin
B
sin
(
A
+
B
)
−
cos
A
=
1
,
2
sin
C
sin
(
B
+
C
)
−
cos
B
=
0
2\sin C\sin (B+C)-\cos B=0
2
sin
C
sin
(
B
+
C
)
−
cos
B
=
0
find the three angles.
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