Đáp án: $x = \frac{{k2\pi }}{{21}}\left( {k \in Z} \right)$
Giải thích các bước giải:
$\begin{array}{l}
cos5x + {\sin ^2}x = {\cos ^2}x\\
\Rightarrow \cos 5x = co{s^2}x - {\sin ^2}x\\
\Rightarrow \cos 5x = \cos 2x\\
\Rightarrow \left[ \begin{array}{l}
5x = 2x + k2\pi \\
5x = - 2x + k2\pi
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = \frac{{k2\pi }}{3}\\
x = \frac{{k2\pi }}{7}
\end{array} \right.\left( {k \in Z} \right)\\
\Rightarrow x = \frac{{k2\pi }}{{21}}\left( {k \in Z} \right)
\end{array}$
