ĐKXĐ: \(x\ne\dfrac{\pi}{2}+k\pi\)
\(\sqrt{3}sinx.cosx+cos^2x=1\)
\(\Leftrightarrow\dfrac{\sqrt{3}}{2}sin2x+\dfrac{1}{2}cos2x=\dfrac{1}{2}\)
\(\Leftrightarrow sin\left(2x+\dfrac{\pi}{6}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{\pi}{6}=\dfrac{\pi}{6}+k2\pi\\2x+\dfrac{\pi}{6}=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)
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