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WAEC Further Mathematics 2008 Question 21

Question 21

Trigonometry

Express 1/(1 − sin 45°) in surd form

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

Answer: A (2 + √2)

Explanation

sin 45° = 1/√2, so the expression is √2/(√2 − 1). Multiply top and bottom by (√2 + 1): √2(√2 + 1)/1 = 2 + √2.