\(\Leftrightarrow\frac{1}{2}+\frac{1}{2}cos2x+2sin2x+\frac{3}{2}=0\)
\(\Leftrightarrow cos2x+4sin2x=-4\)
\(\Leftrightarrow\frac{4}{\sqrt{17}}sin2x+\frac{1}{\sqrt{17}}cos2x=-\frac{4}{\sqrt{17}}\)
Đặt \(\frac{4}{\sqrt{17}}=cosa\) với \(a\in\left(0;\pi\right)\)
\(\Rightarrow sin2x.cosa+cos2x.sina=-cosa\)
\(\Leftrightarrow sin\left(2x+a\right)=sin\left(a-\frac{\pi}{2}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+a=a-\frac{\pi}{2}+k2\pi\\2x+a=\frac{3\pi}{2}-a+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{4}+k\pi\\x=\frac{3\pi}{4}-a+k\pi\end{matrix}\right.\)