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UI Post-UTME Mathematics 2019 (Model questions) Question 20

Question 20

Trigonometry

If cos2θ + 1/8 = sin2θ. The value of tan θ is

  1. A.3
  2. B.3√7/7
  3. C.3√7
  4. D.√7
Show the answer and explanation

Answer: B (3√7/7)

Explanation

cos²θ + 1/8 = 1 − cos²θ gives cos²θ = 7/16, so sin²θ = 9/16 and tan θ = (3/4)/(√7/4) = 3/√7 = 3√7/7.