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Number of triangles in which $\tan A+\tan B+\tan C=\cot A+\cot B+\cot C$ is
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Verified Answer
The correct answer is:
0
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.
$\tan A+\tan B+\tan C=\cot A+\cot B+\cot C$
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.
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