Trignometric identities - Express as a single sine or cosine function

Okay, I am having trouble understanding how to use trigonometric equations. The question states:

Express as a single sine or cosine function.

i) cos 2a cos a - sin 2a sin a

ii) sin 2m cos m + cos 2m sin m

My attempt:

i) cos 2a cos a - sin 2a cos a

= cos^2 a - sin^2 a cos a - 2sin a cos a sin a

= cos^2 a - 1 - cos^2 a cos a - 2 sin a cos a sin a

I do not know what to do from here. The answer in the book is cos 3a

ii) sin 2m cos m + cos 2m sin m

I do not know where to start with this question.

I was hoping someone could show, as an example, how to answer the first question, and maybe give a few hints as to how to go about answering the second one.

Thank you.