Prove that if are angles of a triangle , then :

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- Sep 10th 2009, 08:23 PMdhiabAngles of a triangle
**Prove that if are angles of a triangle , then :**

- Sep 11th 2009, 10:12 AMred_dog
1)

Let

The discriminant is

2) Is the same inequality because

- Sep 11th 2009, 02:47 PMDavidEriksson
A shorter solution for 1. It's enough to show that it's true for .

Now to the proof for this case. Notice that is a concave on so by Jensens inequality:

with equality iff .