anyone explain how this cos 2A cos A – sin 2A sin A

Question

can become to this

cos (2A + A) = cos 3A

Answer 1

look at the definition of
cos(A+B)

cosAcosB - sinAsinB = cos(A+B)

now compare that to the given
cos2AcosA - sin2AsinA

you will reach the "inescapable" conclusion that it must be
cos(2A+A) or cos 3A

If you want the proof of why the identity is true ....
here is one by Khan
http://khanexercises.appspot.com/video/proof--cos-a-b-----cos-a--cos-b---sin-a--sin-b?playlist=Trigonometry