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The value of the product tan1°·tan2°·tan3° ⋯ tan89° is:

Competition practiceTrigonometry
  • A0
  • B1
  • C45
  • D89

Step-by-Step Solution

Pair each tan k° with tan(90° − k°) = cot k°, so every pair multiplies to 1; the unpaired middle factor tan45° is also 1, so the product is 1.
Answer: B) 1

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