a.
ĐKXĐ: \(\left\{{}\begin{matrix}\dfrac{2+sinx}{1+cosx}\ge0\left(\text{luôn đúng}\right)\\1+cosx\ne0\end{matrix}\right.\)
\(\Rightarrow cosx\ne-1\)
\(\Rightarrow x\ne\pi+k2\pi\)
b.
\(\left\{{}\begin{matrix}cos2x\ne0\\sinx+1\ne0\\sin\left(3x+\dfrac{\pi}{6}\right)\ne0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x\ne\dfrac{\pi}{2}+k\pi\\x\ne-\dfrac{\pi}{2}+k2\pi\\3x+\dfrac{\pi}{6}\ne k\pi\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x\ne-\dfrac{\pi}{2}+k2\pi\\x\ne-\dfrac{\pi}{18}+\dfrac{k\pi}{3}\end{matrix}\right.\)
c.
\(\left\{{}\begin{matrix}cos5x\ne0\\sin4x-cos3x\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}cos5x\ne0\\sin4x\ne sin\left(\dfrac{\pi}{2}-3x\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x\ne\dfrac{\pi}{2}+k\pi\\4x\ne\dfrac{\pi}{2}-3x+k2\pi\\4x\ne3x-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{10}+\dfrac{k\pi}{5}\\x\ne\dfrac{\pi}{14}+\dfrac{k2\pi}{7}\\x\ne-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
