Example 1. Given $\cos ^{2} \alpha+\cos ^{2} \beta=\mathrm{m}$, find the value of $\cos (\alpha+\beta)$ - $\cos (\alpha-\beta)$.
Solve $\begin{array}{l}\cos (\alpha+\beta) \cos (\alpha-\beta)=\cos ^{2} \alpha-\sin ^{2} \beta \\ \quad=\cos ^{2} \alpha-\left(1-\cos ^{2} \beta\right) \\ =\cos ^{2} \alpha+\cos ^{2} \beta-1=\mathrm{m}-1 .\end{array}$