Consider the following statements: 1. In a triangle ABC, if cotA·cotB·cotC > 0, then the triangle is an acute angled triangle. 2. In a triangle ABC, if tanA·tanB·tanC > 0, then the triangle is an obtuse angled triangle. Which of the above statements is/are correct?

In an acute triangle, all angles are < 90°, so all cotangents are positive, and cotA·cotB·cotC > 0. Conversely if cotA·cotB·cotC > 0, then either all three cotangents are positive (acute triangle) or two are negative (impossible in a triangle where at most one angle exceeds 90°). So statement 1 is correct. For statement 2: in any triangle, tanA + tanB + tanC = tanA·tanB·tanC. In an acute triangle, all tangents are positive, so product > 0. So tanA·tanB·tanC > 0 implies acute triangle, not obtuse. Statement 2 is incorrect.