Toán Lớp 11: Giải phương trình: sin2x-4sin4x=0
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Toán Lớp 11: Giải phương trình: sin2x-4sin4x=0
Comments ( 2 )
\sin 2x – 4\sin 4x = 0\\
\Leftrightarrow \sin 2x – 4.2\sin 2x.\cos 2x = 0\\
\Leftrightarrow \sin 2x\left( {1 – 8\cos 2x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 2x = 0\\
\cos 2x = \dfrac{1}{8}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = k\pi \\
2x = \pm \arccos \dfrac{1}{8} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{k\pi }}{2}\\
x = \pm \dfrac{1}{2}\arccos \dfrac{1}{8} + k\pi
\end{array} \right.\\
Vậy\,x = \dfrac{{k\pi }}{2};x = \pm \dfrac{1}{2}\arccos \dfrac{1}{8} + k\pi
\end{array}$