In a triangle ABC \tan A+\tan B+\tan C=k What is the value of \cot A \cot B \cot C?
- A. 0.5k
- B. 1/k ✓
- C. 3/k
- D. 1/k^{3}
Correct Answer: B. 1/k
Explanation
For any triangle ABC, the sum of the angles is 180^{\circ}, which yields the identity \tan A + \tan B + \tan C = \tan A \tan B \tan C. Therefore, we have \tan A \tan B \tan C = k. The required value is \cot A \cot B \cot C = \frac{1}{\tan A \tan B \tan C} = \frac{1}{k}.