Toán Lớp 11: cosx+cos3x+cos5x=0
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Toán Lớp 11: cosx+cos3x+cos5x=0
giúp mình với
Comments ( 1 )
\cos x + \cos 3x + \cos 5x = 0\\
\Leftrightarrow \left( {\cos x + \cos 5x} \right) + \cos 3x = 0\\
\Leftrightarrow 2\cos 3x\cos 2x + \cos 3x = 0\\
\Leftrightarrow \cos 3x\left( {2\cos 2x + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos 3x = 0\\
\cos 2x = – \dfrac{1}{2}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
3x = \dfrac{\pi }{2} + k\pi \\
2x = \dfrac{{2\pi }}{3} + k2\pi \\
2x = – \dfrac{{2\pi }}{3} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{6} + \dfrac{{k\pi }}{3}\\
x = \dfrac{\pi }{3} + k\pi \\
x = – \dfrac{\pi }{3} + k\pi
\end{array} \right.\left( {k \in \mathbb{Z}} \right)
\end{array}$