Trigonometry alevel maths q

Prove that:
cosAcos(A-B) + sinAsin(A-B) = cosB

I started using the trig identity for sin(A-B) and cos(A-B) from the LHS but after that I don't see how the equation would cancel?

From where you left off (again I'm trusting you did everything right so far, since you didn't show your work):
I'm going to guess you missed the fact that cos^2x + sin^2x = 1.

That said, another approach that doesn't expand the cos(A-B) and sin(A-B) is to note that something familiar will pop up if you make a substitution, like C=A-B (but leave the A alone)*.

*You don't need this substitution, but if you can't see it outright, it is helpful to see the structure.

What are you allowed to assume here? If you know the formula for cos(A+B) (or cos(A-B)) there is a one-line substitution that gives you the answer straight away, so it's a bit of a weird question IMHO

Yes, I am given the formula. After expanding it, I realised the terms cancel, then leading to the factorisation of cosB. Although the mark scheme has a different approach which I couldn't make sense of... It mentioned cosAcos(A-B) + sinAsin(A-B) = cos (A- (A-B)) = cosB ?

Prove that:
cosAcos(A-B) + sinAsin(A-B) = cosB

I started using the trig identity for sin(A-B) and cos(A-B) from the LHS but after that I don't see how the equation would cancel?

Yes, I am given the formula. After expanding it, I realised the terms cancel, then leading to the factorisation of cosB. Although the mark scheme has a different approach which I couldn't make sense of... It mentioned cosAcos(A-B) + sinAsin(A-B) = cos (A- (A-B)) = cosB ?