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For any triangle ABC, prove that(a-b)/c=...

For any triangle ABC, prove that`(a-b)/c=(sin((A-B)/2))/(cosC/2)`

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To prove that \(\frac{a-b}{c} = \frac{\sin\left(\frac{A-B}{2}\right)}{\cos\left(\frac{C}{2}\right)}\) for any triangle \(ABC\), we will use the sine rule and some trigonometric identities. ### Step-by-Step Solution: 1. **Start with the Sine Rule**: The sine rule states that: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = k ...
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