Prove the following trigonometric identities.

We have to prove $\frac{\tan A+\tan B}{\cot A+\cot B}=\tan A \tan B$

Now,

$\frac{\tan A+\tan B}{\cot A+\cot B}=\frac{\tan A+\tan B}{\frac{1}{\tan A}+\frac{1}{\tan B}}$

$=\frac{\tan A+\tan B}{\frac{\tan B+\tan A}{\tan A \tan B}}$

$=\tan A \tan B$

Hence proved.