I do not know how to find a single function of x or ø by using an identity. How do you find a single function using identities for a problem such as:

cos(3pi/4 - x)

2 answers

huh? This is a single function!

Not sure what you're getting at...
y = cos(3π/4 - x) already is a single function of x, namely the cosine function.
I don't understand what else you want to do with it.
We know:

using cos(A-B) = cosAcosB + sinAsinB

cos(3π/4 - x) = cos 3π/4 cosx + sin 3π/4 sin x
= -√2/2 cosx + √2/2sinx
= √2/2 (sinx - cosx) , no improvement here.