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Let alpha be a root of the equation (2si...

Let `alpha` be a root of the equation `(2sinx-cosx)(1+cosx)=sin^2x` `beta` is a root of the equation `3cos^2x-10cosx+3=0` `gamma` be a root of the equation `1-sin2x=cosx-sinx` `0<=alpha,beta,gamma<=pi/2``cos alpha+cos beta+cos gamma` can be equal to (A) `3sqrt(6)+2sqrt(2)+6sqrt(2)` (B) `(3sqrt(3)+8)/12` (C) `(3sqrt(3)+2)/6` (D) none of these

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Knowledge Check

  • alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos ^2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 sin alpha + sin beta + sin gamma can be equal to

    A
    `(14-3sqrt(2))/( 6 sqrt(2))`
    B
    `5//6`
    C
    `(3+4sqrt(2))/(6)`
    D
    `(1+sqrt(2))/(2) `

  • alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos 2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 cos alpha + cos beta + cos gamma can be equal to

    A
    `(3sqrt(6)+2sqrt(2)+6)/(6sqrt(2))`
    B
    `(3sqrt(3)-8)/(6)`
    C
    `(3sqrt(3)+2)/(6)`
    D
    None of these

  • alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos 2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 sin (alpha - beta ) is equal to

    A
    1
    B
    0
    C
    `(1-2sqrt(6))/(6)`
    D
    `(sqrt(3)-2sqrt(2))/( 6)`

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    Let A(alpha, 1/(alpha)),B(beta,1/(beta)),C(gamma,1/(gamma)) be the vertices of a DeltaABC where alpha, beta are the roots of the equation x^(2)-6p_(1)x+2=0, beta, gamma are the roots of the equation x^(2)-6p_(2)x+3=0 and gamma, alpha are the roots of the equation x^(2)-6p_(3)x+6=0, p_(1),p_(2),p_(3) being positive. Then the coordinates of the cenroid of DeltaABC is

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