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In triangle ABC, prove that 'tan((B-C)...

In triangle ABC, prove that 'tan((B-C)/2)=(b-c)/(b+c)cotA/2``tan(C-A)/2=(c-a)/(c+a)cotB/2``tan(A-B)/2=(a-b)/(a+b)cotC/2`

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To prove the identities in triangle ABC, we will follow a systematic approach using the sine rule and trigonometric identities. We will prove each identity step by step. ### Step 1: Proving \( \tan\left(\frac{B-C}{2}\right) = \frac{B-C}{B+C} \cot\left(\frac{A}{2}\right) \) 1. **Start with the Sine Rule**: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] ...
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