\({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{{\rm{\alpha }}\cos {\rm{x}}}}{{{\rm{\pi }} - 2{\rm{x}}}}}&{{\rm{if}}}&{{\rm{x}} \ne \frac{{\rm{\pi }}}{2}}\\ 3&{{\rm{if}}}&{{\rm{x}} = \frac{{\rm{\pi }}}{2}} \end{array}} \right.\) which is continuous at \({\rm{x}} = \frac{{\rm{\pi }}}{2}\) where α is a constant.What is the value of α?

• A. 6
• B. 3
• C. 2
• D. 1