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Subject: "Trig Inequality"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #715
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Bractals
Member since Jun-9-03
May-21-09, 06:37 PM (EST)
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"Trig Inequality"
 
   How do you prove the following?

If A, B, and C are the interior angles of a triangle, then

cosA + CosB + cosC <= 3/2.


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alexbadmin
Charter Member
2376 posts
May-22-09, 10:48 AM (EST)
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1. "RE: Trig Inequality"
In response to message #0
 
   cosA + CosB + cosC - 1 = 4 sin(A/2) sin(B/2) sin(C/2) ≤ 1/2

The inequality on the right can be proven by, first reducing it to two angles and then differentiation. There is only one local extremum attained for A = B = C = π/3.


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