If $\cot^{-1} a < \epsilon $ can you tell me why $a> \cot \epsilon$

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If $\cot^{-1} a < \epsilon $ can you tell me why $a> \cot \epsilon$ instead of $a< \cot \epsilon$

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It's wrong.

Try $a=1$ and $\epsilon=3.15.$ Because $$\cot^{-1}1<\pi<3.15,$$ but $$1>\cot3.15$$ is wrong.