1.
ĐKXĐ: \(sin\left(2x+3\right)\ne0\Leftrightarrow2x+3\ne k\pi\)
\(\Leftrightarrow x\ne-\frac{3}{2}+\frac{k\pi}{2}\)
2.
ĐKXĐ: \(\left\{{}\begin{matrix}cos2x\ne0\\sinx\ne-1\\sin\left(3x+\frac{\pi}{6}\right)\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2x\ne\frac{\pi}{2}+k\pi\\x\ne-\frac{\pi}{2}+k2\pi\\3x+\frac{\pi}{6}\ne k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{4}+\frac{k\pi}{2}\\x\ne-\frac{\pi}{2}+k2\pi\\x\ne-\frac{\pi}{18}+\frac{k\pi}{3}\end{matrix}\right.\)
3.
\(\left\{{}\begin{matrix}cos5x\ne0\\sin4x\ne cos3x\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}5x\ne\frac{\pi}{2}+k\pi\\sin4x\ne sin\left(\frac{\pi}{2}-3x\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{10}+\frac{k\pi}{5}\\4x\ne\frac{\pi}{2}-3x+k2\pi\\4x\ne\frac{\pi}{2}+3x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{10}+\frac{k\pi}{5}\\x\ne\frac{\pi}{14}+\frac{k2\pi}{7}\\x\ne\frac{\pi}{2}+k2\pi\end{matrix}\right.\)
