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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 70
Prove this trigonometric inequality
Prove this trigonometric inequality
Source: 2019 Jozsef Wildt International Math Competition
May 20, 2020
trigonometry
inequalities
Problem Statement
If
x
∈
(
0
,
π
2
)
x \in \left(0,\frac{\pi}{2}\right)
x
∈
(
0
,
2
π
)
then
(
sin
(
π
2
sin
x
)
sin
x
)
2
+
(
sin
(
π
2
cos
x
)
cos
x
)
2
≥
3
\left(\frac{\sin \left(\frac{\pi}{2}\sin x\right)}{\sin x}\right)^2+\left(\frac{\sin \left(\frac{\pi}{2}\cos x\right)}{\cos x}\right)^2\geq 3
(
sin
x
sin
(
2
π
sin
x
)
)
2
+
(
cos
x
sin
(
2
π
cos
x
)
)
2
≥
3
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