Question:
Prove the following trigonometric identities.
$\frac{\tan A+\tan B}{\cot A+\cot B}=\tan A \tan B$
Solution:
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.
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