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• Question: sin(x)cos(x)(1 + tan²(x)) =
  (a) tan(x) + 1
  (b) cos(x)
  (c) sin(x)
  (d) tan(x)
  (e) sin(x) + cos(x)
  Answer: sin(x)cos(x)(1 + tan²(x)) =sin(x)cos(x)(1 + sin²(x)/cos²(x)) =

  sin(x)cos(x)[(cos²(x) + sin²(x))/cos²(x)] =

  sin(x)cos(x)[1/cos²(x)] = sin(x)/cos(x) = tan(x)

• Question: For any x such that 0 < x < ¶/2, the expression (1 - sin²x)/cos(x) + (1 – cos²x)/sin(x) is equivalent to:
  
  

  (a) sin(x)
  
  (b) cos(x)
  
  (c) sin(x) – cos(x)
  
  (d) sin(x) + cos(x)
  
  (e) 2sin(x)
  
  

  Answer:
  
  (1 – sin²x)/cos(x) + (1 – cos²x)/sin(x) = cos²x/cos(x) +
  sin²x/sin(x) = sin(x) + cos(x).

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