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Rupal Umar Swaminathan
Asked: 2022-11-05T00:55:01+05:30 In:

Which of the following are the solutons of equations `2sin 11x + cos 3x + sqrt(3) sin 3x = 0` ?
A. `x=(n pi)/(7)-(pi)/(84), n in Z`
B. `x=(n pi)/(4)+(7pi)/(48),n in Z`
C. `x=(n pi)/(7)-(pi)/(63),n in Z`
D. `x = (n pi)/(4)+(pi)/(24),n in Z`

Which of the following are the solutons of equations `2sin 11x + cos 3x + sqrt(3) sin 3x = 0` ?
A. `x=(n pi)/(7)-(pi)/(84), n in Z`
B. `x=(n pi)/(4)+(7pi)/(48),n in Z`
C. `x=(n pi)/(7)-(pi)/(63),n in Z`
D. `x = (n pi)/(4)+(pi)/(24),n in Z`
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1 Answer

  1. Correct Answer – A::B
    `2 sin 11x + cos 3x + sqrt(3) sin 3x =0`
    `rArr (1)/(2)cos 3x + (sqrt(3))/(2)sin 3x + sin 11x = 0`
    `rArr sin (30^(@)+3x) + sin 11x =0`
    `rArr 2sin((pi)/(12)+7x)cos ((pi)/(12)-4x)=0`
    `rArr sin((pi)/(12)+7x)=0` or `cos((pi)/(12)-4x)=0`
    `rArr (pi)/(12)+7x = npi` or `4x-(pi)/(12)=n pi +(pi)/(2), n in Z`
    `rArr x = (n pi)/(7)-(pi)/(84)` or `x =(n pi)/(4)+(7pi)/(48), n in Z`

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