In `DeltaABC`, prove that:
`(b-c)/(a)=(tanB/2-tanC/2)/(tanB/2+tanC/2)`

Explanation

To prove the equation \(\frac{b - c}{a} = \frac{\tan \frac{B}{2} - \tan \frac{C}{2}}{\tan \frac{B}{2} + \tan \frac{C}{2}}\) in triangle \(ABC\), we will follow these steps:

### Step 1: Use the Law of Sines
We start with the Law of Sines, which states:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = k \]
From this, we can express \(a\), \(b\), and \(c\) in terms of \(k\):
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