If sin2θ = cos3θ, where 0&nb

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 Multiple Choice QuestionsMultiple Choice Questions

11.

What is the value of tan75° + cot75°

  • 2

  • 4

  • 23

  • 43


12.

What is the value of cos46°cos47°cos48°cos49°cos50° ... cos135° = ?

  •  - 1

  • 0

  • 1

  • Greater than 1


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13.

If sin2θ = cos3θ, where 0 < θ < π2, then what is sinθ = ?

  • 5 + 14

  • 5 - 14

  • 5 + 116

  • 5 - 116


B.

5 - 14

We have,sin2θ = cos3θsin2θ = cosθ + 2θsin2θ = cosθcos2θ - sinθsin2θ2sinθcosθ = cosθ1 - 2sin2θ - 2sin2θcosθ2sinθ = 1 - 2sin2θ - 2sin2θ4sin2θ + 2sinθ - 1 = 0sinθ =  - 2 ± 22 - 44 - 12 × 4 sinθ =  - 2 ±4 +168sinθ =  - 1 ± 54sinθ = 5 - 14

0 < θ < π2


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14.

If the roots of the equation x2 + px + q = 0 are tan(190) and tan(26°), then which one of the following is correct?

  • q - p = 1

  • p - q = 1

  • p + q = 2

  • p + q = 3


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15.

what is 1 + tanαtanβ2 + tanα - tanβ2 - sec2αsec2β = ?

  • 0

  • 1

  • 2

  • 4


16.

If p = cscθ - cotθ and q = cscθ - cotθ - 1, then which one of the following is correct?

  • pq = 1

  • p = q

  • p + q = 1

  • p + q = 0


17.

What is the least value of 25cosec2(x) + 36sec2(x) ?

  • 1

  • 11

  • 120

  • 121


18.

If sinθ + cosθ = 2cosθ, then what is cosθ - sinθ = ?

  •  - 2cosθ

  •  - 2sinθ

  • 2sinθ

  • 2sinθ


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19.

If sinθ = - 12 and tanθ = 13, Then in which quadrant does θ lie ?

  • First

  • Second

  • Third

  • Fourth


20.

If sinx = 15, siny = 110, where 0 < x < π2, 0 < y <  π2, then what is x + y = ?

  • π

  • π2

  • π4

  • 0


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