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JAMB Mathematics 1982 Question 20

Question 20

Trigonometry

If sin θ = (m − n)/(m + n) find the value of 1 + tan2θ

  1. A.2(m2 + n2)/(m + n)
  2. B.√(2(m2 + n2))/(m + n)
  3. C.(m2 + n2 + 2mn)/2mn
  4. D.(m2 + n2 + 2mn)/4mn
  5. E.(m + n)2/4√(mn)
Show the answer and explanation

Answer: D ((m2 + n2 + 2mn)/4mn)

Explanation

1 + tan²θ = sec²θ = 1/cos²θ. cos²θ = 1 − (m − n)²/(m + n)² = 4mn/(m + n)², so 1 + tan²θ = (m + n)²/4mn = (m² + n² + 2mn)/4mn.