\(\Leftrightarrow1-2\cdot sin\left(\dfrac{x}{2}\right)\cdot cos\left(\dfrac{x}{2}\right)+2\cdot cos^2\left(\dfrac{x}{2}\right)-3=0\)
\(\Leftrightarrow1-sinx+2\cdot\dfrac{1+cosx}{2}-3=0\)
\(\Leftrightarrow1-sinx+1+cosx-3=0\)
\(\Leftrightarrow-sinx+cosx-1=0\)
\(\Leftrightarrow sinx-cosx+1=0\)
\(\Leftrightarrow\sqrt{2}sin\left(x-\dfrac{pi}{4}\right)=-1\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{pi}{4}=-\dfrac{pi}{4}+k2pi\\x-\dfrac{pi}{4}=\dfrac{5}{4}pi+k2pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=k2pi\\x=\dfrac{3}{2}pi+k2pi\end{matrix}\right.\)