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2019 AIME Problems
8
trigonometric extrapolation
trigonometric extrapolation
Source: 2019 AIME I #8
March 14, 2019
AMC
AIME
AIME I
Problem Statement
Let
x
x
x
be a real number such that
sin
10
x
+
cos
10
x
=
11
36
\sin^{10}x+\cos^{10} x = \tfrac{11}{36}
sin
10
x
+
cos
10
x
=
36
11
. Then
sin
12
x
+
cos
12
x
=
m
n
\sin^{12}x+\cos^{12} x = \tfrac{m}{n}
sin
12
x
+
cos
12
x
=
n
m
where
m
m
m
and
n
n
n
are relatively prime positive integers. Find
m
+
n
m+n
m
+
n
.
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