why $\cos\alpha\cos\beta+\sin\alpha\sin\beta=\cos(\beta - \alpha)$? I'm studying linear algebra and there is a chapter in a book that says about unit vector and it says this $$ \cos\alpha \cos\beta + \sin\alpha \sin\beta = \cos(\beta - \alpha) $$ Why?? I'm newbie and need very detail answer. Does the alpha and beta just represent angle a and angle b and has no special meaning???
you can have a look at the attached picture from the book:


Let $u = (\cos \theta, \sin \theta )$, and $v = (\cos \beta, \sin \beta)$, then $u\cdot v = ||u||\cdot ||v||\cdot \cos (\beta - \theta)$, and from this your identity follows.
