\(2sin2x+sinx.cosx-cos^2x+1=0\)
\(\Leftrightarrow4sin2x+2sinx.cosx-2cos^2x+2=0\)
\(\Leftrightarrow4sin2x+sin2x-cos2x=-1\)
\(\Leftrightarrow5sin2x-cos2x=-1\)
\(\Leftrightarrow\sqrt{26}\left(\dfrac{5}{\sqrt{26}}sin2x-\dfrac{1}{\sqrt{26}}cos2x\right)=-1\)
\(\Leftrightarrow cos\left(2x+arccos\dfrac{1}{\sqrt{26}}\right)=\dfrac{1}{\sqrt{26}}\)
\(\Leftrightarrow2x+arccos\dfrac{1}{\sqrt{26}}=\pm arccos\dfrac{1}{\sqrt{26}}+k2\pi\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=-arccos\dfrac{1}{\sqrt{26}}+k\pi\end{matrix}\right.\)
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