A problem in Trigonometry (Properties of Triangles)

[Wrichik Basu]

In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$

 

[Buffu]

In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$

Did you try to solve this ?
Also you should not vandalise the template.

 

[Wrichik Basu]

Did you try to solve this ?
Also you should not vandalise the template.

I tried in several ways, trying to change a, b, c to 2R sin A and like that, or trying the formulae for cot A/2, but got nowhere.

 

[Buffu]

I tried in several ways, trying to change a, b, c to 2R sin A and like that, or trying the formulae for cot A/2, but got nowhere.

Use sine rule and A + B + C = 180.