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If (sin^(3)"" (x)/(2)-cos^(3)""(x)/(2))/...

If `(sin^(3)"" (x)/(2)-cos^(3)""(x)/(2))/(2 + sin x) = (cos x)/( 3) ` then x =

A

`n pi/2 + (pi)/(2), n inZ`

B

`2 n pi + (pi)/(2), n in Z`

C

`n pi - (pi)/(2), n in Z`

D

`2 n pi - (pi)/(2), n in Z`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If 2 sin ^(3) x = cos x then x =

    A
    `x = n pi + (pi)/(4), n in Z`
    B
    `x = n pi + (pi)/( 3), n in Z`
    C
    `x = n pi + (pi)/( 2) , n in Z`
    D
    ` x = n pi + (pi)/( 6) , n in Z`

  • If 7 cos ^(2) x + sin x cos x - 3 then x =

    A
    `x = n pi + (3 pi)/(4), n in Z`
    B
    `x = k pi + tan^(-1) ((4)/(3)), k in Z`
    C
    `x = k + tan^(-1) ((4)/(3)) , k in Z`
    D
    `x = n pi + (pi)/(3), n in Z`

  • If sin^(3) x + sin x .cos x + cos^(3) x = 1 then x =

    A
    `2n pi pm (pi)/(2) : n in Z` or `2n pi : n in Z`
    B
    `n pi pm (pi)/(6) : n in Z` or `n pi pm (pi)/(3) : n in Z`
    C
    `n pi pm (pi)/(3) : n in Z` or `n pi pm (pi)/(2) : n in Z`
    D
    `2n pi + (pi)/(4) : n in Z` or `2n pi : n in Z`

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