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Cosines everywhere (Posted on 2005-03-21) Difficulty: 4 of 5
Prove that in any triangle ABC, 8.cos(A).cos(B).cos(C) < 1.

See The Solution Submitted by Federico Kereki    
Rating: 4.5000 (2 votes)

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re: This problem needs some formatting changes... | Comment 3 of 6 |
(In reply to This problem needs some formatting changes... by Erik O.)

The periods are multiplication signs of a European vogue.  The problem statement is incorrect only in that equality is also possible, as David Shin has pointed out. The product of the cosines of the three angles of a triangle does not exceed .125, although a short ultra-elementary proof seems to me to be very elusive.
  Posted by Richard on 2005-03-23 03:07:33

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