Question

One of the general solutions of `sqrt(3) cos theta-3 sin theta=4 sin 2 theta cos 3 theta` 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

Answer 1

`sqrt3costheta - 3sintheta = 4sin2thetacos3theta`
`=>sqrt3costheta - 3sintheta = 2(2cos3thetasin2theta)`
`=>sqrt3/2costheta - 3/2sintheta = sin5theta - sintheta`
`=>sqrt3/2costheta - 1/2sintheta = sin5theta`
`=>cos(pi/6)costheta - sin(pi/6)sintheta = sin5theta`
`=>cos(theta+pi/6) = cos(pi/2-5theta)`
`=>theta+pi/6 = 2npi+-(pi/2 - 5theta)`
`=>theta = (npi)/3 +pi/18 and theta = -(npi)/2+pi/6`
So, option `c` is the correct option.