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JAMB Mathematics 1987 Question 39

Question 39

Trigonometry

If tan θ = (m2 − n2)/2mn, find sec θ

  1. A.(m2 + n2)/(m2 − n2)
  2. B.(m2 + n2)/2mn
  3. C.mn/(2(m2 + n2))
  4. D.m2n2/(m2 − n2)
Show the answer and explanation

Answer: B ((m2 + n2)/2mn)

Explanation

Take a right triangle with opposite side m² − n² and adjacent side 2mn. The hypotenuse is √((m² − n²)² + 4m²n²) = m² + n², so sec θ = hypotenuse/adjacent = (m² + n²)/2mn.