# $(\cot \alpha)^{\cos 2\alpha} \ge \frac{1}{\sin 2\alpha}$

Let $0< \alpha < \dfrac{\pi}{2}$. Prove: $$(\cot \alpha)^{\cos 2\alpha} \ge \dfrac{1}{\sin 2\alpha}$$

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Since you are new, I want to give some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people are much more willing to help you if you show that you've tried the problem yourself. Please don't use the [homework] tag as the only tag for your question. Also, many would consider your post rude because it is a command ("Prove..."), not a request for help, so please consider rewriting it. –  Zev Chonoles Dec 21 '12 at 14:37
I am VietNamese ; so I bad good at English. –  H.T.H Dec 22 '12 at 5:51
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## 1 Answer

do manipulations by taking logs and reduce it to x^x(1-x)^(1-x)>1/2.Again take log of tis.find derivative and find the local minima or maxima=1/1+e^2 and second derivative which is greater than zero hence minima. not put it in the function and estimate it

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I don't know. Can you help me? Thank you. –  H.T.H Dec 22 '12 at 12:05
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