If \[\sin A=n\sin B,\] then \[\frac{n-1}{n+1}\tan \,\frac{A+B}{2}=\]

• A. \[\sin \frac{A-B}{2}\]
• B. \[\tan \frac{A-B}{2}\]
• C. \[\cot \frac{A-B}{2}\]
• D. None of these