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For problems Let cos^(-1)(4x^(3)-3x)=a+b...

For problems Let `cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x`
If `x in [-1, -1/2)`, then the value of `a+bpi` is

A

`2pi`

B

`3pi`

C

`pi`

D

`-2pi`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in [-1/2, 1/2], then the principal value of sin^(-1)(sin""a/b)

    A
    `-pi/3`
    B
    `pi/3`
    C
    `-pi/6`
    D
    0

  • For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in (1/2,1) then the value of lim_(ytoa)b cos (y) is

    A
    `-1/3`
    B
    `-3`
    C
    `1/3`
    D
    `3`

  • For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in (1/2, 1] , then the value of lim_(y to a)bcos(y) is

    A
    `-1/3`
    B
    -3
    C
    `1/3`
    D
    3

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    Explore conceptually related problems

    If x^2-4x+3=1 then find the value of x.

    The least value of (sin^(-1)x)^3+(cos^(-1)x)^3 is

    {:("Column-I", "Column-II"), ("a) "cos^(-1)(4x^(3)-3x)=3cos^(-1)x", then x can takes values", "p) "[1//2,1]), ("b) "sin^(-1)(3x-4x^(3))=3sin^(-1)x", then x can takes values", "q) "[-1//2,0]), ("c) "cos^(-1)(4x^(3)-3x)=3sin^(-1)x", then x can take values", "r) "[0,sqrt(3)//2]), ("d) "sin^(-1)(3x-4x^(3))=3cos^(-1)x", then x can takes values", "s) "[0, 1//2]):}

    int Cos^(-1)(4x^(3)-3x)dx=

    (d)/(dx)[cos ^(-1)(4x^(3) - 3x)]=

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