Trigonometric identities involve an equal sign with a different expressions on either side.
So it's not clear what exactly you require in your questions. Do you need to simplify the expressions?
I suggest you check for typos as well as I do not see what β has to do with question 1.
1. (2cosx-2secx)(3cosx^2+3secx^2+β)
2. (16tanxsecx-4secx)/(8tanxsecx+4secx)
3.sinxcosx^3+cosx^4 (hint: GCF)
4. (cosβ+sinβ)^2
3 answers
I apologize; it is simplifying. The homework is for my identities unit, though. And number 1 does not have a typo. Sorry!
Typically with simplification like these, you would convert all functions into sine and cosine, and simplify from there on. Use sin²x+cos²x=1 whenever appropriate.