b.
\(\sqrt{3}cosx+sin2x=0\)
\(\Leftrightarrow cosx\left(\sqrt{3}+2sinx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\\sqrt{3}+2sinx=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\sinx=sin\left(\dfrac{-\pi}{3}\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=-\dfrac{\pi}{3}+k2\pi\\x=\pi+\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=\dfrac{-\pi}{3}+k2\pi\\x=\dfrac{4\pi}{3}+k2\pi\end{matrix}\right.\left(k\in Z\right)\)
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