Prove that, in any given triangle, it holds:
![\[(a+b+c)\left(\tan\frac{A}{2}+\tan\frac{B}{2}\right) = 2 c \cot\frac{C}{2}\]](https://www.math.tolaso.com.gr/wp-content/ql-cache/quicklatex.com-ebe42ed4ff4ea9150f68986e8c2d4dd5_l3.png "Rendered by QuickLaTeX.com")
Solution
Using the fact that 
and similarly for the other number, where 
is the semiperimeter of the triangle we have successively:
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Prove that, in any given triangle, it holds:
Solution
Using the fact that and similarly for the other number, where is the semiperimeter of the triangle we have successively: