Prove that: \[ \frac{\tan (A+B)}{\cot (A-B)}=\frac{\tan ^{2} A-\tan ^{2} B}{1-\tan ^{2} A \tan ^...

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Prove that:
\[
\frac{\tan (A+B)}{\cot (A-B)}=\frac{\tan ^{2} A-\tan ^{2} B}{1-\tan ^{2} A \tan ^{2} B}
\]
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