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A + B = 45°, with A and B positive. Find (1 + tan A)(1 + tan B).

Competition practiceTrigonometry
  • A2
  • B1
  • C4
  • D√2

Step-by-Step Solution

tan(A + B) = 1 gives tan A + tan B = 1 − tan A tan B. So (1 + tan A)(1 + tan B) = 1 + (tan A + tan B) + tan A tan B = 2.
Answer: A) 2

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