Toán Lớp 11: Gỉai phương trình sau:
2cos 4x + 8sin 2x = 5
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Toán Lớp 11: Gỉai phương trình sau:
2cos 4x + 8sin 2x = 5
Comments ( 2 )
2\cos 4x + 8\sin 2x = 5\\
\Leftrightarrow 2\left( {1 – 2{{\sin }^2}2x} \right) + 8\sin 2x = 5\\
\Leftrightarrow 2 – 4{\sin ^2}2x + 8\sin 2x = 5\\
\Leftrightarrow 4{\sin ^2}2x – 8\sin 2x + 3 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 2x = \dfrac{1}{2}(tm)\\
\sin 2x = \dfrac{3}{2}(L)
\end{array} \right.\\
\Leftrightarrow \sin 2x = \dfrac{1}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \dfrac{\pi }{6} + k2\pi \\
2x = \dfrac{{5\pi }}{6} + k2\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{{12}} + k\pi \\
x = \dfrac{{5\pi }}{{12}} + k\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$