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Dhiraj Manoj Ray
Asked: 2022-11-05T22:18:13+05:30 In:

If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to
A. `20//9`
B. `2//3`
C. `13//9`
D. `8//9`

If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to
A. `20//9`
B. `2//3`
C. `13//9`
D. `8//9`
Parabola
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  1. Correct Answer – C
    `8 cos x (cos (pi/6+x) cos (pi/6-x)-1/2)=1`
    `rArr 8 cos x [cos^(2) pi/6- sin^(2) x-1/2]=1`
    `rArr 8 cos x [1/4-(1-cos^(2) x)]=1`
    `rArr 8cos^(3)x-6 cos x =1`
    `rArr 4 cos^(3) x-3 cos x=1/2`
    `rArr cos 3 x=1/2=”cos” pi/3`
    `3x=2npi pm pi/3, n in Z`
    Since `x in [0, pi]`, possible values are
    `3x=pi/3, 2pi pm pi/3`
    `:. x=pi/9, (5pi)/9, (7pi)/9`
    sum of solution `=(13 pi)/9`
    `:. k=13/9`

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Nitin Bala
Asked: 2022-11-02T09:28:25+05:30 In:

If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to
A. `13/9`
B. `8/9`
C. `20/9`
D. `2/3`

If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to
A. `13/9`
B. `8/9`
C. `20/9`
D. `2/3`
Parabola
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1 Answer

  1. Correct Answer – A

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