Looking for a strictly trigonometric solution for three-phase systems. Trying to find alternate form for:
$$\sin(x)-\sin(x-120^{\circ})$$
From using WolframAlpha for the expansion:
$$\sin(x)-\sin(x)\cos(120^{\circ})-\cos(x)\sin(120^{\circ})$$
showed an alternate form of:
$$\sqrt{2-2\cos(120^{\circ})}\sin\left(x-\tan^{-1}\left(\frac{\sin(120^{\circ})}{1-\cos(120^{\circ})}\right)\right)$$
This is the form of solution I was looking for although using trigonometric identities I am unable to achieve an answer in this form. Maybe a conversion into another co-ordinate system but honestly have no idea how to proceed. Any help on this would be greatly appreciated.