If \( \tan \mathrm{A}=m \tan \mathrm{B} \), prove that \( \frac{\sin (\mathrm{A}-\mathrm{B})}{\s...

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If \( \tan \mathrm{A}=m \tan \mathrm{B} \), prove that \( \frac{\sin (\mathrm{A}-\mathrm{B})}{\sin (\mathrm{A}+\mathrm{B})}=\frac{m-1}{m+1} \).
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