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 ^^"

The formula holds for all $\alpha,\beta$. If you only know it for the case that $\alpha-\beta>0$ note that for $\alpha-\beta<0$,
$$ \cos(\alpha-\beta)=\cos(\beta-\alpha)=\cos(\beta)\cos(\alpha)+\sin(\beta)\sin(\alpha)$$
(and of course for $\alpha=\beta$, $1=\cos 0=\cos^2(\alpha)+\sin^2(\alpha)$
