已知 cosαcosα−sinα=3\frac{\cos \alpha }{\cos \alpha - \sin \alpha } = \sqrt{3}cosα−sinαcosα=3 ,则 tan(α+π4)=\tan \left( {\alpha + \frac{\pi }{4}}\right) =tan(α+4π)= ( )A. 23+12\sqrt{3} + 123+1B. 23−12\sqrt{3} - 123−1C. 32\frac{\sqrt{3}}{2}23D. 1−31 - \sqrt{3}1−3