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OAU Post-UTME Mathematics 2023 Question 11

Question 11

Trigonometry

Given that sin x = 2/3, evaluate, leaving your answer in surd form, tan x − cos x

  1. A.√3/5
  2. B.2√3/15
  3. C.√5/15
  4. D.2√5/15
Show the answer and explanation

Answer: C (√5/15)

Explanation

With opposite 2 and hypotenuse 3, the adjacent side is √5. So tan x = 2/√5 = 2√5/5 and cos x = √5/3. 2√5/5 − √5/3 = (6√5 − 5√5)/15 = √5/15.