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Balkan MO
1987 Balkan MO
3
easy trigonometry, but strange
easy trigonometry, but strange
Source: bmo 1987
April 23, 2007
trigonometry
geometry open
geometry
Problem Statement
In the triangle
A
B
C
ABC
A
BC
the following equality holds:
sin
23
A
2
cos
48
B
2
=
sin
23
B
2
cos
48
A
2
\sin^{23}{\frac{A}{2}}\cos^{48}{\frac{B}{2}}=\sin^{23}{\frac{B}{2}}\cos^{48}{\frac{A}{2}}
sin
23
2
A
cos
48
2
B
=
sin
23
2
B
cos
48
2
A
Determine the value of
A
C
B
C
\frac{AC}{BC}
BC
A
C
.
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