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Moscow Mathematical Olympiad
1952 Moscow Mathematical Olympiad
231
MMO 231 Moscow MO 1952 cos32x +a_{31}cos3x+... +a_2cos2x+a_1cosx
MMO 231 Moscow MO 1952 cos32x +a_{31}cos3x+... +a_2cos2x+a_1cosx
Source:
August 8, 2019
trigonometry
Sum
algebra
Problem Statement
Prove that for arbitrary fixed
a
1
,
a
2
,
.
.
,
a
31
a_1, a_2,.. , a_{31}
a
1
,
a
2
,
..
,
a
31
the sum
cos
32
x
+
a
31
cos
31
x
+
.
.
.
+
a
2
c
o
s
2
x
+
a
1
cos
x
\cos 32x + a_{31} \cos 31x +... + a_2 cos 2x + a_1 \cos x
cos
32
x
+
a
31
cos
31
x
+
...
+
a
2
cos
2
x
+
a
1
cos
x
can take both positive and negative values as
x
x
x
varies.
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