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Problem
Problem
Prove that
(
tan
−
1
1
e
)
2
+
2
e
e
2
+
1
<
(
tan
−
1
e
)
2
+
2
e
2
+
1
.
\left( \tan^{-1} \frac{1}{e} \right)^2 + \frac{2e}{\sqrt{e^2+1}} < (\tan^{-1} e)^2 + \frac{2}{\sqrt{e^2+1}}.
(
tan
−
1
e
1
)
2
+
e
2
+
1
2
e
<
(
tan
−
1
e
)
2
+
e
2
+
1
2
.
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