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31. If secθ + tanθ = √3 (0° ≤ θ ≤ 90°), then tan3θ is
  A.  undefined
  B.  1/√3
  C.  1/√2
  D.  √3
     
   
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32. If a sinθ + b cosθ = c then the value of a cos θ − b sinθ is:
  A.  ±√(−a2 + 2 + c2
  B.  ±√(a2 + 2 − c2
  C.  ±√(a2 − 2 − c2
  D.  ±√(a2 − 2 + c2
     
   
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33. If sin (A − B) = 1/2 and cos (A + B) =1/2 where A>B>0 and A + B is an acute angle, then the value B is:
  A.  π/6
  B.  π/12
  C.  π/4
  D.  π/2
     
   
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34. The value of 152(sin 30° + 2 cos245° + 3 sin30° + 4 cos2 45° + ...............+ 17 sin 30° + 18 cos2 45°) is
  A.  an integer but not a perfect square
  B.  a rational number but not an integer
  C.  a perfect square of an integer
  D.  irrational
     
   
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35. sin2θ - 3 sinθ + 2 = 0 will be true if
  A.  0° ≤ θ ≤ 90°
  B.  0 < θ < 90°
  C.  θ = 0°
  D.  θ = 90°
     
   
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36. If tan α = n tan β and sin &alpha = m sin &beta, then cos2&alpha is
  A.  m2/n2 + 1
  B.  m2/n2
  C.  m2 − 1/n2 - 1
  D.  m2 + 1/n2 + 1
     
   
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37. If cosecθ &minus cotθ = 7/2, the value of cosecθ is:
  A.  47/28
  B.  51/28
  C.  53/28
  D.  49/28
     
   
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38. If x sin 45° = y cosec 30°, then x4/y4 is equal to
  A.  43
  B.  63
  C.  23
  D.  83
     
   
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39. If 5 tan θ = 4, then 5sinθ − 3 cosθ/5 sinθ +2 cosθ is equal to
  A.  2/3
  B.  1/4
  C.  1/6
  D.  1/3
     
   
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40. 2 cosec223° cot267° − sin223° − sin267° − cot267° is equal to:
  A.  1
  B.  sec223°
  C.  tan223°
  D.  0
     
   
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