A) \[2\tan A\,\,\tan B\,\,\tan C\]
B) \[\tan A\,\,\tan B\,\,\tan C\]
C) \[\cot A\,\,\cot B\,\,\cot C\]
D) \[\tan A\,\,\tan B\,\,\cot C\]
Correct Answer: B
Solution :
We know, \[A+B+C={{180}^{o}}\] or \[A+B={{180}^{o}}-C\] \[\therefore \] \[\tan \,(A+B)=tamn\,({{180}^{o}}-C)\] or \[\frac{\tan A+\tan B}{1-\tan A\tan B}=-\tan C\] or \[tan\,A+tan\,B=-tan\,C+tan\,A\,tan\,B\,tan\,C\] or \[tan\,\,A+tan\,\,B+tan\,\,C=tan\text{ }A\text{ }tan\text{ }B\text{ }tan\text{ }C\]
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