A problem in Trigonometry (Properties of Triangles)

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The discussion centers on proving the trigonometric identity for triangle ABC, specifically the equation involving cotangents and side lengths. Participants express frustration in solving the problem, with one suggesting the use of the sine rule and the angle sum property of triangles. Attempts to manipulate the sides using the circumradius (2R) and cotangent formulas have not yielded results. The conversation emphasizes the complexity of the proof and the need for a strategic approach. The problem remains unresolved, highlighting the challenges in triangle trigonometry.
Wrichik Basu
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In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$
 
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Wrichik Basu said:
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.
 
Buffu said:
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.
 
Wrichik Basu said:
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.
 

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