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How can I prove that for all $t\in[0,\frac{\pi}{2}], \cot^2t\leq\frac{1}{t^2}\leq1+\cot^2t$, with $\cot$ the cotangent function ? Thank you

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    Are you sure you have written the inequality right?2012-01-11
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    Pretty much, yes. Why ?2012-01-11
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    I think we can derive a simpler inequality to prove from the given inequality, and prove it by derivatives or similar.2012-01-11

3 Answers 3