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For which of these pairs is (1 + tanA)(1 + tanB) exactly 2?

Competition practiceTrigonometry
  • AA = 10°, B = 35°
  • BA = 20°, B = 30°
  • CA = 15°, B = 45°
  • DA = 25°, B = 35°

Step-by-Step Solution

The product equals 2 precisely when A + B = 45°, since then tanA + tanB = 1 − tanA·tanB. Only 10° + 35° = 45°. The other pairs sum to 50°, 60° and 60°, and their products are 2.151, 2.536 and 2.493 — close to 2 but never equal to it.
Answer: A) A = 10°, B = 35°

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