If   then the value of  is: from Quantitative Aptitude Tri

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 Multiple Choice QuestionsMultiple Choice Questions

81.

The value of cot space 10 degree. space cot space 20 degree. space cot space 60 degree. space cot space 70 degree. space cot space 80 degree is

  • 1

  • -1

  • square root of 3
  • square root of 3
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82.

If 7 space sin squared straight theta space plus space 3 space cos squared straight theta space equals space 4 comma 0 degree less than straight theta less than 90 degree comma then the value of tan space straight theta is:

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


B.

fraction numerator 1 over denominator square root of 3 end fraction
space space space space 7 sin squared straight theta space plus space 3 cos squared straight theta space equals space space 4
rightwards double arrow space space 7 sin squared straight theta space plus space 3 left parenthesis 1 minus sin squared straight theta right parenthesis space equals space 4
rightwards double arrow space space 7 sin squared straight theta space plus space 3 minus 3 sin squared straight theta space equals space 4
rightwards double arrow space space space space 4 sin squared straight theta space equals space 1
rightwards double arrow space space space space sin squared straight theta space equals space 1 fourth
rightwards double arrow space space space sin space straight theta space equals space 1 half comma space space space space sin space straight theta space equals space sin space 30 degree comma space space space space straight theta space equals 30 degree
therefore space space space tan space straight theta space equals space tan space 30 degree space equals space fraction numerator 1 over denominator square root of 3 end fraction


space
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83.

If sin space left parenthesis 2 straight a space plus space 45 degree right parenthesis space equals space cos space left parenthesis 30 degree space minus space straight a right parenthesis comma where 0° < a < 90°, then the value of a is

  • 0°

  • 15°

  • 45°

  • 45°

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84.

Value of (cos 53° - sin 37°) is

  • 0

  • 1

  • 2sin37°

  • 2sin37°

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85.

If cosec space straight theta space plus space sin space straight theta space equals space 5 over 2, then the value of cosec space straight theta space minus space sin space straight theta is

  • negative 3 over 2
  • 3 over 2
  • negative fraction numerator square root of 3 over denominator 2 end fraction
  • negative fraction numerator square root of 3 over denominator 2 end fraction
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86.

If sec (4x - 50°) = cosec (50° - x), then the value of x is

  • 45°

  • 90°

  • 30°

  • 30°

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87.

If tan space straight theta space equals space 4 over 3 comma then the value of fraction numerator 3 space sinθ space plus space 2 space cosθ over denominator 3 space sinθ space minus space 2 space cosθ end fraction is

  • 1 half
  • 1 1 half
  • 3

  • 3

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88.

If cos2x + cos4x = 1, then tan2x + tan4x = ?

  • 0

  • 1

  • 2tan2x

  • 2tan2x

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89.

If cos 27° = x, then value of 63° is

  • fraction numerator straight x over denominator square root of 1 minus straight x squared end root end fraction
  • fraction numerator straight x over denominator square root of 1 plus straight x squared end root end fraction
  • fraction numerator square root of 1 minus straight x squared end root over denominator straight x end fraction
  • fraction numerator square root of 1 minus straight x squared end root over denominator straight x end fraction
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90.

If θ is a positive acute angle and 7 space cos squared straight theta space plus space 3 space sin squared straight theta space equals space 4 comma then the value of θ is

  • 60°

  • 30°

  • 45°

  • 45°

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