Question

Why does gravity have the x and y components: mg sin theta and mg cos theta : on inclined planes?

Answer 1

Because you take y axis perpendicular to the surface and x axis with the surface, so gravity will be distributed in x and y.

While if you take y with gravity it won't have x component only y.(and in this case you will get components for friction and force ,so it would be longer methods to solve inclined plane problems)