do I have to remember or understand completely on identities (e.g. trig identities)

Hi Ali Aqsa,

no, a computer is not a better calculator than we are and it is 100% important for you to focus as well and try to know at least a proportion of the identities especially if you would like to be an engineer, though you don't have to know everything about it I do believe that you should have a solid understanding of it depending on what type of engineer that you are pursuing.

Hope this helps and if you have any additional questions feel free to ask.