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For every acute angle θ, which pair of expressions is always equal?

Competition practiceTrigonometry
  • Atan(90° − θ) and tanθ
  • Bcos(90° − θ) and cosθ
  • Ccot(90° − θ) and cotθ
  • Dcosec(90° − θ) and secθ

Step-by-Step Solution

Complementary angles swap a ratio with its co-ratio: sin(90° − θ) = cosθ, tan(90° − θ) = cotθ and cosec(90° − θ) = secθ. Only the last pair is listed correctly; the other three each keep the ratio unchanged instead of swapping it.
Answer: D) cosec(90° − θ) and secθ

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