The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not? I'm a beginner student study the proof of sum and difference trigonometry formula.
There is a formula that:
$$\cos(\alpha-\beta) = \cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$$
In the tutorial it shows only the case when $\alpha > \beta$
Can this formula be used when $\alpha < \beta$ ? and is the answer mathematically legitimate? and why it is? or why it is not?
please give me very detail and basic step by step explanation. I'm newbie ^^"

Swap $ \alpha , \beta$ . Has anything happened to the result? No. So cos function's argument can be either >0 or <0, cos is an even function, $\cos(-x)=\cos(x),$ or,
$$ \cos (\alpha-\beta)  = \cos ( \beta -\alpha ) $$
