Đáp án:
\[\cos \left( {a + b} \right).cos\left( {a - b} \right) = \frac{{ - 119}}{{144}}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\cos a.\cos b = \frac{1}{2}\left( {\cos \left( {a + b} \right) + \cos \left( {a - b} \right)} \right)\\
\Rightarrow \cos \left( {a + b} \right).cos\left( {a - b} \right)\\
= \frac{1}{2}.\left( {\cos \left( {a + b + a - b} \right) + \cos \left( {a + b - a + b} \right)} \right)\\
= \frac{1}{2}\left( {\cos 2a + \cos 2b} \right)\\
= \frac{1}{2}.\left( {2{{\cos }^2}a - 1 + 2{{\cos }^2}b - 1} \right)\\
= {\cos ^2}a + {\cos ^2}b - 1\\
= {\left( {\frac{1}{3}} \right)^2} + {\left( {\frac{1}{4}} \right)^2} - 1 = \frac{{ - 119}}{{144}}
\end{array}\)
