Tính giá trị biểu thức  \(A = \cos \frac{{5\pi }}{{12}}\cos \frac{{7\pi }}{{12}}\).             

Chọn C

Ta có:

  \[\begin{array}{l}A = \cos \frac{{5\pi }}{{12}}\cos \frac{{7\pi }}{{12}} = \frac{1}{2}\left[ {\left( {\cos \frac{{5\pi }}{{12}} - \frac{{7\pi }}{{12}}} \right) + \left( {\cos \frac{{5\pi }}{{12}} + \frac{{7\pi }}{{12}}} \right)} \right]\\ = \frac{1}{2}\left( {\cos \frac{{ - 2\pi }}{{12}} + \cos \frac{{12\pi }}{{12}}} \right) = \frac{1}{2}\left( {\cos \frac{{ - \pi }}{6} + \cos \pi } \right) = \frac{1}{2}.\left( {\frac{{\sqrt 3 }}{2} - 1} \right).\end{array}\]