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Hi, I am curious to kow about this smoothing concept that I've seen mentioned somewhere but do not understand. It would be great if someone could explain it to me, preferably through a solution to this problem. Thanks for any comments. (Latex did not generate in the preview, so if it seems there was a mistake with the code, please tell which was it.)

Let [tex] a_0,...,a_n [/tex] be real numbers in the interval [tex](0, \frac{\pi}{2})[/tex] such that

[tex]\[\tan (a_0 - \dfrac{\pi}{4})+...+\tan (a_n-\dfrac{\pi}{4})\geq n - 1\][/tex]

Prove that

[tex]\[\tan(a_0)\tan(a_1)...tan(a_n) \geq n^{n + 1}\][/tex]

Let [tex] a_0,...,a_n [/tex] be real numbers in the interval [tex](0, \frac{\pi}{2})[/tex] such that

[tex]\[\tan (a_0 - \dfrac{\pi}{4})+...+\tan (a_n-\dfrac{\pi}{4})\geq n - 1\][/tex]

Prove that

[tex]\[\tan(a_0)\tan(a_1)...tan(a_n) \geq n^{n + 1}\][/tex]

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