singing to the rhythm of life.
please tell what is the mistake?
Without the context, it is difficult to tell. Those words alone do not constitute a sentence, so it may help to have the rest of it.
As a gut reaction, I would say that you normally sing "to" another person, or to an audience. You can "sing along" to a song on the radio, which can also be said to be "singing along with..."
You can, of course, dance or move TO a rhythm.
More info please!