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Which of the following are the solutons ...

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`

Text Solution

Verified by Experts

The correct Answer is:
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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