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WAEC Mathematics 1999 Question 27

Question 27

Trigonometry

If tan x = 1/√3, find cos x − sin x such that 0° ≤ x ≤ 90°

  1. A.(√3 + 1)/2
  2. B.2/(√3 + 1)
  3. C.(√3 − 1)/2
  4. D.2/(√3 − 1)
Show the answer and explanation

Answer: C ((√3 − 1)/2)

Explanation

tan x = 1/√3 means x = 30°. cos 30° − sin 30° = √3/2 − 1/2 = (√3 − 1)/2.