Been working a little problem here for a while, the whole thing looks like this:

Simplify:

sin(x)/tan(x) + cos(x)tan(x)

I know the right side can be simplified to sin(x), but im not sure about the left. I put it into terms of cosine and sine, making it: sin(x)/sin(x)/cos(x)

My thought process here was to then multiply by the reciprocal, which would end with the sin(x)'s cancelling out and leaving just cos(x).

Can anyone verify this?