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16 sin x cosx cos 2x cos 4x cos 8x in...

`16 sin x cosx cos 2x cos 4x cos 8x in`

A

`[-1,1]`

B

`[-(1)/(4), (1)/(4)]`

C

`[-(3)/(4), (3)/(4)]`

D

`[-(sqrt(3))/(2), (sqrt(3))/(2)]`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If f(x) = cos x cos 2x cos 4x cos 8x cos 16 x then f^1((pi)/(4)) equals

    A
    `sqrt(2)`
    B
    `0`
    C
    `1/(sqrt(2))`
    D
    `"Cosec" pi/4`
  • The period of the function f(x)=( sin 8x cos x-sin 6x cos 3x )/(cos 2x cos x- sin 3x sin 4x ) is

    A
    `(pi)/4`
    B
    `(pi)/2`
    C
    `pi`
    D
    `(3pi)/2`
  • The general solution of the equation 8 cos x cos 2x cos 4x=sin 6x/sinx is

    A
    `x =(n pi/7)+(pi//21), AA n in Z`
    B
    `x =(2pi//7)+(pi//14), AA n in Z`
    C
    `x=(n p //7)+(pi//14), AA n in Z`
    D
    `x =(n pi )+(pi//14), AA n in Z`
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    A : cos 24^(@) cos 48^(@) cos 96^@ cos 168^(@) = 1//16 R : cos x cos 2 x cos 4x ........ cos (2^n x)=( sin (2^(n+1)x))/(2^(n+1) sin x )