The value of 1 + sin2π9 + i

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 Multiple Choice QuestionsMultiple Choice Questions

301.

If 1 + tanα1 + tan4α = 2, α  0, π16,then α = ?

  • π20

  • π30

  • π40

  • π50


302.

If cosθ = cosα - cosβ1 - cosαcosβ, then one of the values of tanθ2 is

  • cotβ2tanα2

  • tanα2tanβ2

  • tanβ2cotα2

  • tan2α2tan2β2


303.

The value of the expression 1 + sin2αcos2α - 2πtanα - 3π4 - 14sin2αcotα2 + cot3π2 + α2 is

  • 0

  • 1

  • sin2α2

  • sin2α


304.

If 16sinθ, cosθ and tanθ are in geometric progression, then the solution set of θ is

  • 2 ± π6

  • 2 ± π3

  •  +  - 1nπ3

  •  + π3


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305.

In ABC if x = tanB - C2tanA2, y = tanC - A2tanB2 and  z = tanA - B2tanC2, then x + y+ z = ?

  • xyz

  • - xyz

  • 2xyz

  • 12xyz


306.

If A > 0, B > 0 and A + B = π3, then the maximum value of AtanB is

  • 13

  • 13

  • 12

  • 3


307.

 In ABC, if bcosθ = c - a, (where θ is an acute angle), then (c - a) tanθ = ?

  • 2cacosB2

  •  2acsinB2

  •  2cacosB2

  • 2casinB2


308.

If tanα and  tanβ are the roots of the equation x2 + px + q = 0, then the value ofsin2α + β + pcosα + βsinα + β + qcos2α + β

  • p + q

  • p

  • q

  • pp + q


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309.

1 + cos10° + cos20° + cos30° = ?

  • 4sin10°sin20°sin30°

  • 4cos5°cos10°cos15°

  • 4cos10°cos20°cos30°

  • 4sin5°sin10°sin15°


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310.

The value of 1 + sin2π9 + icos2π91 + sin2π9 - icos2π93 is : 

  • - 123 - i

  • 123 - i

  •  121 - i3

  • - 121 - i3


A.

- 123 - i

1 + cos5π18 +isin5π181 + cos5π18 -isin5π183 = 2cos25π36 + 2isin5π36cos5π362cos25π36 - 2isin5π36cos5π363= cos5π36 +isin5π36cos5π36 -isin5π363 = cos5π36 +isin5π366= cos6 × 5π36 + isin6 × 5π36 = cos5π6 +isin5π6 - 32 + i12


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