Giá trị cos ( a + b ) ⋅ cos ( a − b ) bằng

10/21

Biết \(\cos a = \frac{1}{3}\), \(\cos b = \frac{1}{4}\). Giá trị \[\cos \left( {a + b} \right) \cdot \cos \left( {a - b} \right)\] bằng

\[ - \frac{{113}}{{144}}.\]

\[ - \frac{{115}}{{144}}.\]

\[ - \frac{{117}}{{144}}.\]

\[ - \frac{{119}}{{144}}.\]

Giải thích

Ta có \[\cos \left( {a + b} \right) \cdot \cos \left( {a - b} \right) = \frac{1}{2}\left[ {\cos 2a + \cos 2b} \right]\].

\(\cos 2a = 2{\cos ^2}a - 1 = - \frac{7}{9}\); \(\cos 2b = 2{\cos ^2}b - 1 = - \frac{7}{8}\).

Do đó \[\cos \left( {a + b} \right) \cdot \cos \left( {a - b} \right) = \frac{1}{2}\left[ {\cos 2a + \cos 2b} \right] = \frac{1}{2}\left( { - \frac{7}{9} - \frac{7}{8}} \right) = - \frac{{119}}{{144}}\]. Chọn D.