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Baltic Way
2010 Baltic Way
2
cos, sin, tan and cot inequality
cos, sin, tan and cot inequality
Source: Baltic Way 2010
November 19, 2010
inequalities
trigonometry
inequalities proposed
Problem Statement
Let
x
x
x
be a real number such that
0
<
x
<
π
2
0<x<\frac{\pi}{2}
0
<
x
<
2
π
. Prove that
cos
2
(
x
)
cot
(
x
)
+
sin
2
(
x
)
tan
(
x
)
≥
1
\cos^2(x)\cot (x)+\sin^2(x)\tan (x)\ge 1
cos
2
(
x
)
cot
(
x
)
+
sin
2
(
x
)
tan
(
x
)
≥
1
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