- #1
sharpycasio
- 16
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Homework Statement
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]
Homework Equations
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.