Trigonometrical ratios of compound angles If $\tan A + \tan B = b$ and $\cot A + \cot B = a$ and $A+B = Y$. Eliminate A and B. I can't understand how to proceed? Please someone help!

Hint:

Write both $\cot$ as $\dfrac1{\tan}$

$$\dfrac ba=?$$

$$\tan Y=\tan(A+B)=?$$