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 Multiple Choice QuestionsMultiple Choice Questions

61.

If 2 space sin space open parentheses πx over 2 close parentheses space equals space straight x squared space plus space 1 over straight x squared comma then the value of open parentheses straight x minus 1 over straight x close parentheses is

  • -1

  • 2

  • 1

  • 1

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62.

If 0 degree space less than space straight theta space less than space 90 degree, the value of sin θ + cos θ is

  • equal to 1

  • greater than 1

  • less than 1

  • less than 1

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63.

If θ is a positive acute angle and tan 2θ tan 3θ = 1, then the value of 
left parenthesis 2 space cos squared straight theta fraction numerator 5 straight theta over denominator 2 end fraction minus 1 right parenthesis is

  • negative 1 half
  • 1

  • 0

  • 0


C.

0

tan 2θ. tan 3θ = 1
rightwards double arrow space space space tan space 3 straight theta space equals space fraction numerator 1 over denominator tan space 2 straight theta end fraction space equals space cot space 2 straight theta
rightwards double arrow space space space tan space 3 straight theta space equals space tan space left parenthesis 90 degree minus 2 straight theta right parenthesis
rightwards double arrow space space space 3 straight theta space equals space 90 degree space minus space 2 straight theta space space space rightwards double arrow space space space 5 straight theta space equals space 90 degree
rightwards double arrow space space space space straight theta space equals space 18 degree

therefore space space space space 2 space cos squared fraction numerator 5 straight theta over denominator 2 end fraction minus 1 space equals space 2 cos squared 45 degree space minus space 1
equals space 2 space cross times space 1 half space minus space 1 space equals space 0

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64.

If sin space 17 degree space equals space straight x over straight y comma then the value of left parenthesis sec space 17 degree space minus space sin space 73 degree right parenthesis is

  • fraction numerator straight y squared over denominator straight x square root of straight y squared minus straight x squared end root end fraction
  • fraction numerator straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction
  • fraction numerator straight x squared over denominator straight y square root of straight x squared minus straight y squared end root end fraction
  • fraction numerator straight x squared over denominator straight y square root of straight x squared minus straight y squared end root end fraction
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65.

In a right-angled triangle, XYZ, right-angled at Y, If XY space equals space 2 square root of 6 and XZ - YZ = 2, then sec X + tan X is

  • fraction numerator 1 over denominator square root of 6 end fraction
  • square root of 6
  • 2 square root of 6
  • 2 square root of 6
311 Views

66.

If tan θ - cot θ = 0 and θ is positive acute angle, then the value of fraction numerator tan space left parenthesis straight theta space plus space 15 degree right parenthesis over denominator tan space left parenthesis straight theta space minus 15 degree right parenthesis end fraction is

  • 3

  • fraction numerator 1 over denominator square root of 3 end fraction
  • 1 third
  • 1 third
173 Views

67.

If sec space straight theta space minus space tan space straight theta space equals space fraction numerator 1 over denominator square root of 3 end fraction comma the value of sec space straight theta. space space tan space straight theta is

  • 2 over 3
  • fraction numerator 2 over denominator square root of 3 end fraction
  • fraction numerator 4 over denominator square root of 3 end fraction
  • fraction numerator 4 over denominator square root of 3 end fraction
359 Views

68.

If 5 space cos space straight theta space plus space 12 space sin space straight theta space equals space 13,  0 degree less than straight theta less than 90 degree comma then the value of sin space straight theta is

  • 5 over 13
  • negative 12 over 13
  • 6 over 13
  • 6 over 13
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69.

If sin A + sin2A = 1,  then the value of cos2A + cos4A is

  • 2

  • 1 2 over 3
  • 1 1 half
  • 1 1 half
155 Views

70.

If 7 space sin squared straight theta space plus space 3 cos squared straight theta space equals space 4, then the value of tan θ is (θ is acute)

  • fraction numerator 1 over denominator square root of 3 end fraction
  • fraction numerator 1 over denominator square root of 2 end fraction
  • square root of 3
  • square root of 3
155 Views

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