Giải PT: sin3x+2cos3x+cos2x-2sin2x-2sinx-1=0

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1. Giải thích các bước giải:

   $\begin{array}{l}
   \sin 3x + 2\cos 3x + \cos 2x – 2\sin 2x – 2\sin x – 1 = 0\\
   \Leftrightarrow \left( {3\sin x – 4{{\sin }^3}x} \right) + \left( {4{{\cos }^3}x – 3\cos x} \right) + \left( {1 – 2{{\sin }^2}x} \right) – 4\cos x.\sin x – 2\sin x – 1 = 0\\
   \Leftrightarrow \sin x – 2{\sin ^2}x – 4{\sin ^3}x + 4{\cos ^3}x – 3\cos x – 4\sin x.\cos x = 0\\
   \Leftrightarrow \left( {\sin x + 2\cos x} \right)\left( {4\cos 2x – 2\sin x – 3} \right) = 0\\
   \Leftrightarrow \left[ \begin{array}{l}
   \sin x + 2\cos x = 0\\
   4\cos 2x – 2\sin x – 3 = 0
   \end{array} \right.\\
   \Leftrightarrow \left[ \begin{array}{l}
   \frac{1}{{\sqrt 3 }}\sin x + \frac{2}{{\sqrt 3 }}\cos x = 0\\
   4 – 8{\sin ^2}x – 2\sin x – 3 = 0
   \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
   \cos \left( {x – \arccos \frac{2}{{\sqrt 3 }}} \right) = 0\\
   \sin x = \frac{1}{4}\\
   \sin x = \frac{{ – 1}}{2}
   \end{array} \right.\\
   \Leftrightarrow \left[ \begin{array}{l}
   x = \pm \left( {\arccos \frac{2}{{\sqrt 3 }} + \frac{\pi }{2}} \right) + k2\pi \\
   x = \left( {\pi – } \right)\arcsin \frac{1}{4} + k2\pi \\
   x = \frac{{ – \pi }}{6} + k2\pi \\
   x = \frac{{7\pi }}{6} + k2\pi
   \end{array} \right.\\

   \end{array}$

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