The general solution of x - 3 2x + 3x = x - 3 2x + 3x & is

We have,

$\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$

$⇒ \sin x + \sin 3x - 3\sin 2x = \cos x + \cos 3x - 3\cos 2x$

$⇒ 2\sin 2xcosx - 3\sin 2x - 2\cos 2xcosx + 3\cos 2x = 0$

$⇒ \sin 2x ( 2\cos x - 3 ) - \cos 2x ( 2\cos x - 3 ) = 0$

$⇒ ( \sin 2x - \cos 2x ) ( 2\cos x - 3 ) = 0$

$⇒ \sin 2x = \cos 2x [ ∵ \cos x \ne 3 / 2 ]$

⇒ 2x = 2n\pi \pm \left(\dfrac{π}{2} -2x\right)$</p><p>$⇒ x = $\dfrac{n\pi}{2} + \dfrac{π}{8}~[$∵~neglect&- ve& sign]