Multiple choice

In a triangle ABC, A = 45°, then the value of (1 + cot

  1. 0

  2. 1
    • 1

  4. 2
    • 2
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D Correct answer
AI explanation

In any triangle, the sum of angles B and C equals 180 degrees minus 45 degrees, which is 135 degrees, making cot of the sum equal to cot 135, or negative 1. Using the tangent addition formula, this means the quantity (cot B times cot C minus 1) divided by (cot B plus cot C) equals negative 1, which simplifies to cot B times cot C equaling negative 1. Expanding the given expression (1 plus cot B) times (1 plus cot C) results in 1 plus cot B plus cot C plus cot B times cot C, and substituting the known product value makes the entire expression equal 2.

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