Đáp án:
$\left[\begin{array}{l}x = k\dfrac{\pi}{3}\\x = k\dfrac{\pi}{7}\end{array}\right.\,\,\,\,\,(k \in \Bbb Z)$
Giải thích các bước giải:
$\begin{array}{l} cos^22x + sin^25x = 1\\ \Leftrightarrow \dfrac{1 + cos4x}{2} + \dfrac{1 - cos10x}{2} = 1\\ \Leftrightarrow cos4x - cos10x = 0\\ \Leftrightarrow cos4x = cos10x\\ \Leftrightarrow \left[\begin{array}{l}4x = 10x + k2\pi\\4x = -10x + k2\pi\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x = k\dfrac{\pi}{3}\\x = k\dfrac{\pi}{7}\end{array}\right.\,\,\,\,\,(k \in \Bbb Z)\end{array}$
