If  the value of  is (where ): from Quantitative Aptitude

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If sec space straight theta space equals space cosec space straight ϕ with 0 degree less than space straight theta comma space space straight ϕ space less than space 90 degree, then the value of sin left parenthesis straight theta plus straight ϕ right parenthesis is

  • 1

  • 0

  • 2

  • 2

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22.

If in a triangle ABC, sinA = cosB then the value of cos C is

  • fraction numerator square root of 3 over denominator 2 end fraction
  • 0

  • 1

  • 1

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23.

If sin space straight theta space cross times space cos space straight theta space equals space 1 half comma space the value of sin space straight theta space minus space cos space straight theta is (where 0 degree less than straight theta less than 90 degree):

  • 0

  • square root of 2
  • 2

  • 2


A.

0

sin space straight theta space cross times space cos space straight theta space equals space 1 half
2 space sin space straight theta space cos space straight theta space equals space 1
space space space sin space 2 straight theta space equals space sin space 90 degree
space space space space space space space space space 2 straight theta space equals space 90 degree
space space space space space space space space space space straight theta space equals space 45 degree
therefore space space sin space straight theta space minus space cosθ space equals space sin space 45 degree space minus space cos space 45 degree
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator square root of 2 end fraction minus fraction numerator 1 over denominator square root of 2 end fraction space equals space 0
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24.

The value of fraction numerator sinθ over denominator 1 plus cosθ end fraction plus fraction numerator sin begin display style straight theta end style over denominator 1 minus cosθ end fraction is

  • 2 sinθ
  • 2 cosθ
  • 2 secθ
  • 2 secθ
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25.

If tan space straight theta space equals space 8 over 15 comma the value of fraction numerator square root of 1 minus sin space straight theta end root over denominator square root of 1 plus sin space straight theta end root end fraction is

  • 1 fifth
  • 2 over 5
  • 3 over 5
  • 3 over 5
207 Views

26.

If fraction numerator cosθ space over denominator 1 minus sinθ end fraction plus fraction numerator cos begin display style space end style begin display style straight theta end style over denominator 1 plus sin space straight theta end fraction space equals space 4 then the value of straight theta left parenthesis 0 less than straight theta less than 90 degree right parenthesis is

  • 60 degree
  • 45 degree
  • 30 degree
  • 30 degree
199 Views

27.

If straight x space equals space straight a space cosθ space plus space straight b space sinθ and straight y equals straight b space cosθ space minus space straight a space sinθ, then straight x squared plus straight y squared is equal to

  • ab

  • straight a squared plus straight b squared
  • straight a squared minus straight b squared
  • straight a squared minus straight b squared
228 Views

28.

If x tan 60° + cos 45° = sec 45° then the value of (x2 + 1) is

  • 6 over 7
  • 7 over 6
  • 5 over 6
  • 5 over 6
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29.

x, y be two acute angles, x + y < 90° and sin (2x - 20°) = cos (2y + 20°), the value of tan (x + y) is

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

  • 1

721 Views

30.

If a2sec2x - b2tan2x = c2 then the value of (sec2x + tan2x) is equal to (assume b2 ≠ a2)

  • fraction numerator straight b squared minus straight a squared plus 2 straight c squared over denominator straight b squared plus straight a squared end fraction
  • fraction numerator straight b squared plus straight a squared minus 2 straight c squared over denominator straight b squared minus straight a squared end fraction
  • fraction numerator straight b squared minus straight a squared minus 2 straight c squared over denominator straight b squared plus straight a squared end fraction
  • fraction numerator straight b squared minus straight a squared minus 2 straight c squared over denominator straight b squared plus straight a squared end fraction
1219 Views

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