Phương trình lượng giác khó

D

demon311

$\sin x \cos 2x - \cos x \cos 2x - 2\cos 2x = \sin x + \cos x \\
\leftrightarrow \cos 2x(\sin x-\cos x-2)-(\sin x+\cos x)=0 \\
\leftrightarrow (\cos x+sin x)[(\cos x-\sin x)(\sin x-\cos x-2)-1]=0 \\
\leftrightarrow \left[ \begin{array}{ll}
\cos x+\sin x=0 \\
-2+2\sin x \cos x -2\cos x+2\sin x=0
\end{array} \right. \\
\leftrightarrow \left[ \begin{array}{ll}
x=-\dfrac{ \pi}{4}+k\pi \\
\sin x \cos x -\cos x+\sin x-1=0
\end{array} \right. $
 
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