Đáp án:
\(S = \left\{k\dfrac{\pi}{5}\ \Bigg|\ k\in\Bbb Z\right\}\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad \sin^23x = \sin^22x\\
\Leftrightarrow \dfrac{1 - \cos6x}{2} = \dfrac{1-\cos4x}{2}\\
\Leftrightarrow \cos6x = \cos4x\\
\Leftrightarrow \left[\begin{array}{l}6x = 4x + k2\pi\\6x = - 4x + k2\pi\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = k\pi\\x = k\dfrac{\pi}{5}\end{array}\right.\\
\Leftrightarrow x = k\dfrac{\pi}{5}\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{k\dfrac{\pi}{5}\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)
