Question

Let $A+B+C=\pi$ then the value of $\frac{\tan A+\tan B+\tan C}{\tan A.\tan B.\tan C}$ is

• A. $-1$
• B. $0$
• C. $1$
• D. none of these

Answer 1

Answer: (C)

$1$

Given

$A+B+C=\pi$

This gives,

$\tan (A+B+C)=0$

or, $\frac{\tan A+\tan B+\tan C-\tan A.\tan B.\tan C}{1-\tan A.\tan B-\tan B.\tan C-\tan C.\tan A}=0$

or, $\tan A+\tan B+\tan C=\tan A.\tan B+\tan C$

or, $\frac{\tan A+\tan B+\tan C}{\tan A.\tan B.\tan C}=1$.