Đáp án:
$\begin{array}{l}
C = \cos x.\cos 2x + \sin 7x.\sin x\\
= \dfrac{1}{2}.2.\cos \dfrac{{3x - x}}{2}.\cos \dfrac{{3x + x}}{2}\\
+ \dfrac{1}{2}.2.\sin \dfrac{{8x + 6x}}{2}.sin\dfrac{{8x - 6x}}{2}\\
= \dfrac{1}{2}.cos\left( {3x + x} \right) - \dfrac{1}{2}.\cos \left( {8x - 6x} \right)\\
= \dfrac{1}{2}.\cos 4x - \dfrac{1}{2}.\cos 2x\\
= \dfrac{1}{2}.\left( {\cos 4x - \cos 2x} \right)\\
= \dfrac{1}{2}.\left( {2{{\cos }^2}2x - 1 - \cos 2x} \right)\\
= \dfrac{1}{2}.\left( {2\cos 2x + 1} \right)\left( {\cos 2x - 1} \right)
\end{array}$
