If xcosθ + ysinθ = z, t

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 Multiple Choice QuestionsMultiple Choice Questions

61.

If  A = cos12° - cos36°sin96° + sin24° and B = sin60° - sin12°cos48° - cos72°, then what is AB = ?

  •  - 1

  • 0

  • 1

  • 2


62.

sinA + sin2A + sin3A is equal to which of thfollowing ?

1. 4sin2Acos2A2

2. 2sin2AsinA2 + cosA22

3. 8sinAcosAcos2A2

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


63.

If x = sin70° . sin50° and y = cos60° . cos80°, then what is xy = ?

  • 116

  • 18

  • 14

  • 12


64.

If sinθ1 + sinθ2 + sinθ3 + sinθ4 = 4, then what is the value of :

cosθ1 + cosθ2 + cosθ3 + cosθ4 ?

 

  • 0

  • 1

  • 2

  • 4


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65.

What is the value of :

1 + cosπ81 + cos3π81 + cos5π81 + cos7π8 ?

  • 12

  • 12 + 122

  • 12 - 122

  • 18


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66.

If xcosθ + ysinθ = z, then what is the value of

xsinθ - ycosθ2 ?

  • x2 + y2 - z2

  • x2 - y2 - z2

  • x2 - y2 + z2

  • x2 + y2 + z2


A.

x2 + y2 - z2

 xcosθ + ysinθ = zsquaring both sidesx2cos2θ + y2sin2θ + 2xysinθcosθ = z2         ...iNow, xsinθ - ycosθ2 = m2 supposex2sin2θ + y2cos2θ - 2xysinθcosθ = m2  ... iiAdding i and iix2cos2θ +sin2θ  + y2sin2θ + cos2θ              = z2 + m2x2 + y2 = z2 + m2       m2 = x2 + y2 - z2Hence, xsinθ - ycosθ2 = x2 + y2 + z2


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67.

If A = x   : x2 + 6x - 7 < 0 and B = x   : x2 + 9x + 14 > 0,

then which of the following is/are correct ?

1. A  B = x  R : - 2 < x < 12. AB = x R : - 7 < x < - 2

Select the correct answer using the code given below :

  • 1 only

  • 2 only

  • both 1 and 2

  • neither 1 nor 2


68.

If sin18° = 5 - 14, then what is the value of sin 81° ?

  • 3 + 5 + 5 - 54

  • 3 +5 + 5 + 54

  • 3 -5 + 5 - 54

  • 3 +5 - 5 - 54


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69.

What is 1 - tan2° . cot62°tan152° - cot88° = ?

  • 3

  • - 3

  • 2 - 1

  • 1 - 2


70.

What is tan25°tan15° + tan15°tan50° + tan25°tan50° = ?

  • 0

  • 1

  • 2

  • 4


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