Toán Lớp 11: giải cos3x-sinx= căn 3 . ( cosx-sin3x)
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Toán Lớp 11: giải cos3x-sinx= căn 3 . ( cosx-sin3x)
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\cos 3x – \sin x = \sqrt 3 \times \left( {xosx – \sin 3x} \right)\\
\Leftrightarrow cos3x + \sqrt {3sin3x} = \sqrt {3cosx} + sinx\\
\Leftrightarrow \frac{1}{2}\cos 3x + \frac{{\sqrt 3 }}{2}\sin 3x = \frac{{\sqrt 3 }}{2}\cos x + \frac{1}{2}\sin x\\
\Leftrightarrow \cos \left( {3x – \frac{\pi }{3}} \right) = \cos \left( {x – \frac{\pi }{6}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
3x – \frac{\pi }{3} = x – \frac{\pi }{6} + k2\pi \\
3x – \frac{\pi }{3} = \frac{\pi }{6} – x + k2\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{{12}} + k\pi \\
x = \frac{\pi }{8} + k2\pi
\end{array} \right.\left( {k \in } \right)\\
\end{array}\]