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UI Post-UTME Mathematics 2025 (Model questions) Question 12

Question 12

Trigonometry

If tan θ + cot θ = 10/3, where 0° < θ < 90°, find sin 2θ

  1. A.4/5
  2. B.3/10
  3. C.3/5
  4. D.4/10
Show the answer and explanation

Answer: C (3/5)

Explanation

tan θ + cot θ = 1/(sin θ cos θ) = 10/3, so sin θ cos θ = 3/10 and sin 2θ = 2 sin θ cos θ = 3/5.