Question

If $A+B+C=\pi$ then $\frac{\tan A+\tan B+\tan C}{\tan A\tan B\tan C}=$

• A. 0
• B. 2
• C. 1
• D. -1

Answer 1

The correct option is C 1

Given, $A+B+C=\pi \Rightarrow \tan (A+B+C)=\tan \pi$
$\Rightarrow \frac{\tan A+\tan B+\tan C-\tan A\tan B\tan C}{1-\tan A\tan B-\tan B\tan C-\tan A\tan C}=0$
$\Rightarrow \tan A+\tan B+\tan C-\tan A\tan B\tan C=0$
$\Rightarrow \frac{\tan A+\tan B+\tan C}{\tan A\tan B\tan C}=1$