Question

Giải phương trình : \(2sin^22x+2sin^2x=3\)

Answer 1

\(\Leftrightarrow2\left(1-cos^22x\right)=2+\left(1-2sin^2x\right)\)

\(\Leftrightarrow2-2cos^22x=2+cos2x\)

\(\Leftrightarrow2cos^22x+cos2x=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\cos2x=-\dfrac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{\pi}{2}+k\pi\\2x=\pm\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x=\pm\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)