Question

In a triangle $ABC$, if $\tan A+\tan +B+\tan C=6$ and $\tan A\tan B=2$, then the triangle is

• A. right angled
• B. isosceles
• C. acute angled
• D. obtuse angled

Answer 1

The correct option is C

acute angled

$A+B+C=\pi \Rightarrow \tan (A+B)=-\tan C\Rightarrow \tan C=3\Rightarrow \tan A+\tan C=3\cdots \left(1\right)$

Given
$\tan A\tan B=2\cdots \left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$A<90°,B<90°,C<90°$