$\tan A-\tan B=x$and $\cot B-\cot A=4$, then $\cot (A-B)=$

Solution:

$y=\cot B-\cot A=\frac{1}{\tan B}-\frac{1}{\tan A}=\frac{x}{\tan A\tan B}$

$\Rightarrow \tan A\tan B=\frac{x}{y}$

Now, 

$\cot (A-B)=\frac{1}{\tan (A-B)}$

$=\frac{1+\tan A\tan B}{\tan A-\tan B}=\frac{1+\frac{x}{y}}{x}=\frac{1}{x}+\frac{1}{y}$