If $\cos A=m\cos B$ and $\cot\large\frac{A+B}{2}$$=\lambda\tan\large\frac{B-A}{2}$ then $\lambda$ is

Question

$\begin{array}{1 1}(a)\;\large\frac{m}{m-1}&(b)\;\large\frac{m+1}{m}\\(c)\;\large\frac{m+1}{m-1}&(d)\;None\; of \;these\end{array}$