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. `m pi+pi//18, m in Z`
B. `mpi//2 +pi//6, AA m in Z`
C. `m pi//3 + pi//18, m in Z`
D. none of these

Answer

C

Explanation

We have `sqrt(3) cos theta-3 sin theta=2(sin 5 theta - sin theta)`
or `(sqrt(3)//2) cos theta-(1//2) sin theta = sin 5 theta`
or `cos (theta+pi//6)= sin 5 theta=cos (pi//2-5 theta)`
`rArr theta+pi//6=2n pi pm (pi//2-5 theta), n in Z`
`rArr theta=(n pi//3)+(pi//18)`
or `theta=(-n pi//2)+(pi//6), AA n in Z`