Cho \(\cos \alpha = \frac{3}{4}\). Tính \(\cos \frac{{3\alpha }}{2}\cos \frac{\alpha }{2}\).

Đáp án đúng là: C

\(\cos \frac{{3\alpha }}{2}\cos \frac{\alpha }{2} = \frac{1}{2}\left[ {\cos \left( {\frac{{3\alpha }}{2} + \frac{\alpha }{2}} \right) + \cos \left( {\frac{{3\alpha }}{2} - \frac{\alpha }{2}} \right)} \right] = \frac{1}{2}\left( {\cos 2\alpha + \cos \alpha } \right)\)

\( = \frac{1}{2}\left( {2{{\cos }^2}\alpha - 1 + \cos \alpha } \right) = \frac{1}{2}\left( {2 \cdot \frac{9}{{16}} - 1 + \frac{3}{4}} \right) = \frac{7}{{16}}\).