Yes, they are the main ones.
A lot can be derived just from these.
Your teacher may push you to remember a whole heap more - I mean ones that you can derive.
It depends how quick you can get as to whether you memorize more or not.
You probably haven't done any calculus yet but I am just youwing you the bit where you will need to rearrage trig.
In calculus you may be asked to integrate cos^2x
You can't do this unless you change it.
\(cos(2x)=sin^2x-cos^2x\\ cos(2x)=1-cos^2x-cos^2x\\ cos(2x)=1-2cos^2x\\ 1-2cos^2x=cos(2x)\\ 1-cos(2x)=2cos^2x\\ cos^2x=\frac{1-cos(2x)}{2}\\ cos^2x=\frac{1}{2}-\frac{cos(2x)}{2}\\\)
The RHS you can integrate.
Now you will probably be told to memorize this resultant rearrangement.
I work it out EVERY time. But my method is slow.