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One side times 3 equals the sum of the other two: product of cotangents of two half-angles

The same question, asked 2 times: 20 Apr 2025 S2, 22 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    124
    In a triangle ABC, with usual notations, 3b=a+c3b=a+c, then cot⁡A2⋅cot⁡C2=\cot\frac{A}{2}\cdot \cot\frac{C}{2}=

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  2. Question 2

    22 Apr 2025 S2

    135
    In a triangle ABC with usual notations, if 3a=b+c3a = b + c, then cot⁡B2⋅cot⁡C2=\cot\frac{B}{2}\cdot \cot\frac{C}{2}=

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