Question

Tìm tất cả nghiệm phương trình : \(sin^2x+sin^23x-2cos^22x=0\) .

Answer 1

\(\Leftrightarrow\frac{1}{2}-\frac{1}{2}cos2x+\frac{1}{2}-\frac{1}{2}cos6x-cos4x-1=0\)

\(\Leftrightarrow\frac{1}{2}\left(cos2x+cos6x\right)+cos4x=0\)

\(\Leftrightarrow cos4x.cos2x+cos4x=0\)

\(\Leftrightarrow cos4x\left(cos2x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos4x=0\\cos2x=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=\frac{\pi}{2}+k\pi\\2x=\pi+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{8}+\frac{k\pi}{4}\\x=\frac{\pi}{2}+k\pi\end{matrix}\right.\)