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UI Post-UTME Mathematics 2021 (Model questions) Question 21

Question 21

Trigonometry

If x + y = 90, simplify (sin x + sin y)2 − 2 sin x sin y

  1. A.0
  2. B.1
  3. C.−1
  4. D.2
Show the answer and explanation

Answer: B (1)

Explanation

sin y = sin(90° − x) = cos x, so the expression is (sin x + cos x)² − 2 sin x cos x = sin²x + cos²x = 1.