A) \[\tan B\]
B) \[2\tan B\]
C) \[\cot B\]
D) \[2\cot B\]
Correct Answer: C
Solution :
\[2\,\,\tan \,(A-B)=2\,\left( \frac{\tan A-\tan B}{1+\tan A\tan B} \right)\] \[=2\frac{(2\tan B+\cot B-\tan B)}{1+(2\,\tan B+\cot B)\,\tan B}=2\,\frac{\tan B+\cot B}{2\,(1+{{\tan }^{2}}B)}\] \[=\frac{\cot B\,({{\tan }^{2}}B+1)}{(1+{{\tan }^{2}}B)}=\cot B\].
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