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For any triangle ABC, prove that sin\ (B...

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

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To prove that \(\sin\left(\frac{B-C}{2}\right) = \frac{b-c}{a} \cos\left(\frac{A}{2}\right)\), we will follow these steps: ### Step 1: Use the Law of Sines According to the Law of Sines, we have: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = k \] where \(k\) is a constant. ...
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