$$\frac{{{\text{cos }}\alpha }}{{{\text{sin }}\beta }} = n$$and $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = m,$$then the value of $${\text{co}}{{\text{s}}^2}\beta $$is?

• A. $\frac{{{m^2} - 1}}{{{n^2} - 1}}$$
• B. $\frac{{{m^2} - 3}}{{{n^2} - 4}}$$
• C. $\frac{{{m^2} + 3}}{{{n^2} + 3}}$$
• D. $\frac{{{n^2}}}{{{m^2} + {n^2}}}$$