(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the angles a, b, c of each triangle satisfy this inequality.

[itex]\tan \frac{a}{2}\tan \frac{b}{2} \tan \frac{c}{2} (\tan \frac{a}{2} + \tan \frac{b}{2} + \tan \frac{c}{2}) < \frac{1}{2}[/itex]

2. Relevant equations

3. The attempt at a solution

I used the half angle formula: [itex] \tan \frac{\theta}{2} = \frac{1- \cos x}{\sin x} [/itex]

That gives

[tex]\frac{(1- \cos a)(1- \cos b)(1- \cos c)}{(\sin a)(\sin b)(\sin c)} [\frac{1- \cos a}{\sin a} + \frac{1- \cos b}{\sin b} + \frac{1- \cos c}{\sin c}] < \frac{1}{2}[/tex]

I don't know where to go from this. Can someone give me any hints please? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove this inequality for all triangles

**Physics Forums | Science Articles, Homework Help, Discussion**