Multiple Choice Question (MCQ)
In ∆ABC, if cotA ⋅cotB ⋅cotC > 0, then the triangle

✓
Acute angled

×
Right angled

×
Obtuse angled

×
Does not exist
In ∆ABC, if cotA ⋅cotB ⋅cotC > 0, then the triangle
Acute angled
Right angled
Obtuse angled
Does not exist
If \cot A \cdot \cot B \cdot \cot C>0, then the triangle ABC is an acute angle triangle.
This is because, in a triangle, the three angles are either all acute or exactly one of them is obtuse. If all three angles are acute, then \cot A, \cot B, and \cot C are all positive, and so their product is also positive. On the other hand, if one angle is obtuse, then the corresponding cotangent will be negative, which means the product of the three cotangents will be negative.
Therefore, if \cot A \cdot \cot B \cdot \cot C>0, the triangle ABC must be acute angled.
So A is correct opinion.