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The value of tan5°·tan25°·tan30°·tan65°·tan85° is:

Competition practiceTrigonometry
  • A1
  • B√3
  • C1/3
  • D1/√3

Step-by-Step Solution

Pair complementary angles: tan5°·tan85° = tan5°·cot5° = 1 and tan25°·tan65° = 1. Only tan30° = 1/√3 survives.
Answer: D) 1/√3

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