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Purple Comet Problems
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25
Purple Comet HS Problem 25
Purple Comet HS Problem 25
Source:
April 12, 2018
trigonometry
Purple Comet
Problem Statement
For
n
n
n
measured in degrees, let
T
(
n
)
=
cos
2
(
3
0
∘
−
n
)
−
cos
(
3
0
∘
−
n
)
cos
(
3
0
∘
+
n
)
+
cos
2
(
3
0
∘
+
n
)
T(n) = \cos^2(30^\circ -n) - \cos(30^\circ -n)\cos(30^\circ +n) +\cos^2(30^\circ +n)
T
(
n
)
=
cos
2
(
3
0
∘
−
n
)
−
cos
(
3
0
∘
−
n
)
cos
(
3
0
∘
+
n
)
+
cos
2
(
3
0
∘
+
n
)
. Evaluate
4
∑
n
=
1
30
n
⋅
T
(
n
)
.
4\sum^{30}_{n=1} n \cdot T(n).
4
n
=
1
∑
30
n
⋅
T
(
n
)
.
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