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National High School Mathematics League
1994 National High School Mathematics League
8
Trigonometry
Trigonometry
Source: 1994 National High School Mathematics League, Exam One, Problem 8
March 2, 2020
trigonometry
Problem Statement
x
,
y
∈
[
−
π
4
,
π
4
]
,
a
∈
R
x,y\in\left[-\frac{\pi}{4},\frac{\pi}{4}\right],a\in\mathbb{R}
x
,
y
∈
[
−
4
π
,
4
π
]
,
a
∈
R
. If
x
3
+
sin
x
−
2
a
=
0
,
4
y
3
+
sin
y
cos
y
+
a
=
0
x^3+\sin x-2a=0,4y^3+\sin y \cos y+a=0
x
3
+
sin
x
−
2
a
=
0
,
4
y
3
+
sin
y
cos
y
+
a
=
0
, then
cos
(
x
+
2
y
)
=
\cos (x+2y)=
cos
(
x
+
2
y
)
=
________.
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