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JAMB Mathematics 1983 Question 8

Question 8

Trigonometry

Given that cos z = L, where z is an acute angle, find an expression for (cot z − cosec z)/(sec z + tan z)

  1. A.(1 − L)/(1 + L)
  2. B.(L2 − √(1 − L2))/(L2 + L − 1)
  3. C.−L√(1 − L)/(√(1 + L)(1 + √(1 − L2)))
  4. D.√(L − 1)/(√(1 − L2) + 1 − L2)
  5. E.L(L − 1)/(1 + √(1 − L2) − L2)
Show the answer and explanation

Answer: E (L(L − 1)/(1 + √(1 − L2) − L2))

Explanation

With sin z = √(1 − L²): cot z − cosec z = (L − 1)/sin z and sec z + tan z = (1 + sin z)/L. Dividing gives L(L − 1)/(sin z + sin²z) = L(L − 1)/(√(1 − L²) + 1 − L²).