已知 α,β\alpha ,\betaα,β 均为锐角,且 cos(α+β)=sinαsinβ\cos \left( {\alpha + \beta }\right) = \frac{\sin \alpha }{\sin \beta }cos(α+β)=sinβsinα ,则 tanα\tan \alphatanα 的最大值是（ ）A. 4B. 2C. 24\frac{\sqrt{2}}{4}42D. 25\frac{\sqrt{2}}{5}52