What is the length of the chord of a unit circle which subtends a

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 Multiple Choice QuestionsMultiple Choice Questions

71.

What is cotA + cscA = ?

  • tanA2

  • cotA2

  • 2tanA2

  • 2cotA2


72.

What is cotA2 - tanA2 = ?

  • tan(A)

  • cot(A)

  • 2tan(A)

  • 2cot(A)


73.

If angle C of a triangle ABC is a right angle, then what is tan(A ) + tan(B) equal to ?

  • a2 - b2ab

  • a2bc

  • b2ca

  • c2ab


74.

What is cos80° + cos40° - cos20° = ?

  • 2

  • 1

  • 0

  • - 19


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75.

If 2tan(A) = 3tan(B) = 1, then what is tan (A B) equal to ?

  • 15

  • 16

  • 17

  • 19


76.

What is sin(α + β) - 2sinαcosβ + sin (α - β) equal to ?

  • 0

  • 2sinα

  • 2sinβ

  • sinα + sinβ


77.

If tan(A) – tan(B) = x and cot(B) – cot(A) = y, then what is the value of cot(A B) ?

  • 1x + 1y

  • 1y - 1x

  • xyx + y

  • 1 + 1xy


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78.

What is the length of the chord of a unit circle which subtends an angle θ at the centre ?

  • sinθ2

  • cosθ2

  • 2sinθ2

  • 2cosθ2


C.

2sinθ2

We have, chord AB of unit circle subtends an angle θ at the centre.

Here radius is 1 because of unit circle.

In OAC and OBC, 

OA = OB = 1 and AC = CB [ if from a centre a perpendicular is drawn to the chord, then a chord is divided by means of congruency.]

When all the sides of triangle OAC and OBC are same then angles are also same are same then angles are also same

  AOC = BOC = θ2

In  OAC,sinθ2 = ACOA    sinθ = Perpendicularhypotenuse AC = 1 . sinθ2Chord length is AB = 2AC = 2sinθ2


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79.

Consider the following statements :

1) cos(θ) + sec(θ) can never be equal to 1.5

2) tan(θ) + cot(θ) can never be less than 2

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


80.

If If cscθ = 2921 where 0 < θ < 90°, then what is the value of 4secθ + 4tanθ = ?

  • 5

  • 10

  • 15

  • 20


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