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If 3cotθ = 4, then the value of (5sinθ − 3cosθ) / (5sinθ + 3cosθ) is:

Competition practiceTrigonometry
  • A1/3
  • B3/5
  • C1/9
  • D9

Step-by-Step Solution

cotθ = 4/3 gives sinθ = 3/5 and cosθ = 4/5. The numerator is 3 − 12/5 = 3/5 and the denominator is 3 + 12/5 = 27/5, so the ratio is 1/9.
Answer: C) 1/9

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