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National High School Mathematics League
1999 National High School Mathematics League
13
Inequality
Inequality
Source: 1999 National High School Mathematics League, Exam One, Problem 13
March 10, 2020
inequalities
Problem Statement
If
x
2
cos
θ
−
x
(
1
−
x
)
+
(
1
−
x
)
2
sin
θ
>
0
x^2\cos\theta-x(1-x)+(1-x)^2\sin\theta>0
x
2
cos
θ
−
x
(
1
−
x
)
+
(
1
−
x
)
2
sin
θ
>
0
for all
x
∈
[
0
,
1
]
x\in[0,1]
x
∈
[
0
,
1
]
, find the range value of
θ
\theta
θ
.
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