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OAU Post-UTME Mathematics 2022 (Batch A) Question 9

Question 9

Trigonometry

Without using calculator, find the value of cos105°

  1. A.(√2 + √6)/4
  2. B.(√2 − √6)/4
  3. C.(√6 + √2)/2
  4. D.(√6 − √2)/2
Show the answer and explanation

Answer: B ((√2 − √6)/4)

Explanation

cos(60° + 45°) = cos60 cos45 − sin60 sin45 = (½)(√2/2) − (√3/2)(√2/2) = (√2 − √6)/4.