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1问题在非钝角△ABC中,证明不等式(1-cos2A)(1-cos2B)1-cos2C+(1-cos2C)(1-cos2A)1-cos2B+(1-cos2B)(1-cos2C)1-cos2A≥94.此题为2006年国家队培训题,在《走向IMO》一书中有它的证明,但笔者认为证明过程太复杂.下面给出一个简洁证明.证明上式即证:∑sin2Bsin2Asin2C≥94左边=(c
1 Problem In the non-obtuse angle △ABC, prove the inequality (1-cos2A)(1-cos2B)1-cos2C+(1-cos2C)(1-cos2A)1-cos2B+(1-cos2B)(1-cos2C)1-cos2A ≥94. This title is a training question for the 2006 national team. It is proved in the book “Towards IMO”, but the author believes that the certification process is too complicated. The following gives a concise proof. Prove that the formula is proof: ∑sin2Bsin2Asin2C≥ 94 left=(c