One of the general solutions of `sqrt(3)costheta-3s intheta=4sin2thetacos3theta` is `mpi+pi/(18),m in Z` `(mpi)/2+pi/6,AAm in Z` `m` `pi/3+pi/(18),m in Z` none of these

Options

A. `(3n pm 1) pi//12, AA n in Z`
B. `(4n pm 1) pi//9, AA n in Z`
C. `(3n pm 1) pi//9, AA n in Z`
D. `(3n pm 1) pi//3, AA n in Z`

Answer

C

Explanation

We have `4 sin theta sin 2 theta sin 4 theta =3 sin theta -4 sin^(3) theta`
or `sin theta [4 sin 2 theta sin 4 theta -3 +4 sin^(2) theta]=0`
or `sin theta [2(cos 2 theta - cos 6 theta)-3+2 (1- cos 2 theta)]=0`
or `sin theta (-2 cos 6 theta -1)=0`
or `sin theta =0 or cos 6 theta =-1//2`
`rArr theta = n pi or 6 theta =2 n pi pm 2 pi//3, AA n in Z`
`= n pi or theta =(3n pm 1) pi//9, AA n in Z`