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In triangle ABC, if angle C is an obtuse angle, which of the following is true?

1. tan A × tan B < 1
2. tan A × tan B ≤ 1
3. tan A × tan B > 1
4. None of these

Correct answer: tan A × tan B < 1

Solution

In a triangle with an obtuse angle, the sum of the angles A and B must be less than 90 degrees. This leads to the product of their tangents being less than 1, as the tangent function is positive and increasing in the first quadrant.

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