are these identities correct?

First one needs an equals sign.

3rd one from the bottom should be cos2x = 2cos^2x - 1 (so the last two are also incorrect).

The way to remember which way round to write the cos2x identities (i.e. whether it's cos2x = 2cos^2x - 1 or if it's cos2x = 2sin^2x - 1 or if it's cos2x = 1 - 2sin^2x or if it's cos2x = 1 - 2cos^2x) is to plug in x = 0. You know that cos(2x) at x = 0 is just 1, so the right hand side should also be 1 (1 - 2cos^2x = 1 - 2 = -1 at x = 0, so it can't be cos2x).