Toán Lớp 11: Giải giúp mình với ak.
Giải phương trình
Sin4x + Sin6x + Sin10x = 0
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Toán Lớp 11: Giải giúp mình với ak.
Giải phương trình
Sin4x + Sin6x + Sin10x = 0
Comments ( 1 )
x = \dfrac{{k\pi }}{5}\\
x = \dfrac{\pi }{6} + \dfrac{{k\pi }}{3}\\
x = – \dfrac{\pi }{4} + \dfrac{{k\pi }}{2}
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\)
\sin x + \sin y = 2\sin \dfrac{{x + y}}{2}.\cos \dfrac{{x – y}}{2}\\
\sin 2x = 2\sin x.\cos x\\
\sin 4x + \sin 6x + \sin 10x = 0\\
\Leftrightarrow \left( {\sin 6x + \sin 4x} \right) + \sin \left( {2.5x} \right) = 0\\
\Leftrightarrow 2.\sin \dfrac{{6x + 4x}}{2}.\cos \dfrac{{6x – 4x}}{2} + 2\sin 5x.\cos 5x = 0\\
\Leftrightarrow 2\sin 5x.\cos x + 2\sin 5x.\cos 5x = 0\\
\Leftrightarrow 2\sin 5x.\left( {\cos x + \cos 5x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 5x = 0\\
\cos x + \cos 5x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 5x = 0\\
\cos 5x = – \cos x
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 5x = 0\\
\cos 5x = \cos \left( {\pi – x} \right)
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
5x = k\pi \\
5x = \pi – x + k2\pi \\
5x = x – \pi + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{k\pi }}{5}\\
6x = \pi + k2\pi \\
4x = – \pi + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{k\pi }}{5}\\
x = \dfrac{\pi }{6} + \dfrac{{k\pi }}{3}\\
x = – \dfrac{\pi }{4} + \dfrac{{k\pi }}{2}
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)
\end{array}\)