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Any triangle, Trigonometric function - second episode! (Posted on 2007-11-18) Difficulty: 3 of 5
Prove that in any triangle cos(A)+cos(B)+cos(C)>1

See The Solution Submitted by Chesca Ciprian    
Rating: 3.0000 (1 votes)

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Some Thoughts non-Euclidean case? | Comment 3 of 12 |
I can not positively state that in any triangle is cos(A) + cos(B) + cos(C) > 1. Consider those triangles in non-Euclidean metrics where the sum of the angles of the triangle is less than 180 degrees.  I am not completely familiar with trigonometric functions in non-Euclidean metrics (though I did discover they exist), thus I wonder if the proposition, cos(A)+cos(B)+cos(C)>1, still holds true for any triangle.
  Posted by Dej Mar on 2007-11-19 04:50:37
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