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WAEC Further Mathematics 2011 Question 21

Question 21

Surds

Evaluate 1/(1 − sin 60°) leaving your answer in surd form.

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

Answer: D (4 + 2√3)

Explanation

1/(1 − √3/2) = 2/(2 − √3). Multiply top and bottom by 2 + √3: 2(2 + √3)/(4 − 3) = 4 + 2√3.