Prove that .

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Prove that (tan⁡−11e)2+2ee2+1<(tan⁡−1e)2+2e2+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}}.

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