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How to show:

In a acute angled $\triangle \ ABC$ show that $$\tan(A) \cdot \tan(B)\cdot \tan(C) \geq 3\sqrt{3}$$

Any ideas?

  • 4
    Use $\tan A \cdot \tan B \cdot \tan C = \tan A + \tan B + \tan C$, and the AM-GM inequality.2011-08-13
  • 1
    The question http://math.stackexchange.com/questions/8732/how-to-prove-this-trignometrical-identities includes the identity Srivatsan mentions.2011-08-13

3 Answers 3