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IMO Longlists
1967 IMO Longlists
39
39
Part of
1967 IMO Longlists
Problems
(1)
sines fraction and cosines fraction
Source: IMO Longlist 1967, Poland 5
10/14/2005
Show that the triangle whose angles satisfy the equality
s
i
n
2
(
A
)
+
s
i
n
2
(
B
)
+
s
i
n
2
(
C
)
c
o
s
2
(
A
)
+
c
o
s
2
(
B
)
+
c
o
s
2
(
C
)
=
2
\frac{sin^2(A) + sin^2(B) + sin^2(C)}{cos^2(A) + cos^2(B) + cos^2(C)} = 2
co
s
2
(
A
)
+
co
s
2
(
B
)
+
co
s
2
(
C
)
s
i
n
2
(
A
)
+
s
i
n
2
(
B
)
+
s
i
n
2
(
C
)
=
2
is a rectangular triangle.
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