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

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put on hold as off-topic by 900 sit-ups a day, Ivo Terek, Tomás, Adam Hughes, anorton yesterday

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I am VietNamese ; so I bad good at English. –  H.T.H Dec 22 '12 at 5:51

1 Answer 1

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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