Prove that in any triangle cos(A)+cos(B)+cos(C)>1

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