Number of triangles in which $\tan A+\tan B+\tan C=\cot A+\cot B+\cot C$ is
Number of triangles in which $\tan A+\tan B+\tan C=\cot A+\cot B+\cot C$ is
1
$\infty$
0
2
Solution
Given,
$\tan A+\tan B+\tan C=\cot A+\cot B+\cot C$
It is possible only when one of the angle is $45^{\circ}$ and sum of other two angles is $90^{\circ}$.
$
\therefore \quad A+B+C=135^{\circ} < 180^{\circ}
$
Hence, no triangle is possible