Question

$A+B+C=\frac{\pi }{2}$, then $\tan A\tan B+\tan B\tan C+\tan A\tan C=$

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is A $1$

Given $A+B+C=\frac{\pi }{2}$
$A+B=\frac{\pi }{2}-C$
$\Rightarrow \frac{\tan A+\tan B}{1-\tan A\tan B}=\cot C=\frac{1}{\tan C}$
$\Rightarrow \tan A\tan C+\tan B\tan C+\tan A\tan B=1$