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2001 Swedish Mathematical Competition
3
cos(A--C) + 4 cos B = 3 if b = (a+c)/2
cos(A--C) + 4 cos B = 3 if b = (a+c)/2
Source: 2001 Swedish Mathematical Competition p3
March 21, 2021
geometry
trigonometry
Problem Statement
Show that if
b
=
a
+
c
2
b = \frac{a+c}{2}
b
=
2
a
+
c
in the triangle
A
B
C
ABC
A
BC
, then
cos
(
A
−
C
)
+
4
cos
B
=
3
\cos (A-C) + 4 \cos B = 3
cos
(
A
−
C
)
+
4
cos
B
=
3
.
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