If \[\alpha ,\beta \]are the roots of the equation \[{{u}^{2}}-2u+2=0\]and if \[\cot \theta =x+1\], then \[[{{(x+\alpha )}^{n}}-{{(x+\beta )}^{n}}]/[\alpha -\beta ]\]is equal to

• A. \[\frac{\sin n\theta }{{{\sin }^{n}}\theta }\]
• B. \[\frac{\cos n\theta }{{{\cos }^{n}}\theta }\]
• C. \[\frac{\sin n\theta }{{{\cos }^{n}}\theta }\]     
• D. \[\frac{\cos n\theta }{{{\sin }^{n}}\theta }\]