Trig Identity: How do I go about proving this?

cos3x = cos^3 x - sin^2 xcosx

Here's how far I am:

cos3x = cos^3 x - sin^2 xcosx

cosx(cos^2 x - sin^2 x)

cosx(cos2x)

Not sure how I go about combining these at this point.

Alternatively, I also tried using the other side:

cos3x =

cos2xcosx - sin2xsinx =

(cos^2 x - sin^2 x)(cosx) - 2sin^2 xcosx

cos^3 x - sin^2 xcosx - 2sin^2 xcosx

cos^ 3 - 3sin^2 xcosx

Help. I have no idea what to do at this point.