## Giúp mk vs các cậu ơi

Question

Giúp mk vs các cậu ơi

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8 tháng 2020-10-15T17:13:04+00:00 1 Answers 71 views 0

${1)x = \dfrac{\pi }{4} + k\dfrac{\pi }{2};x = \dfrac{\pi }{{42}} + k\dfrac{{2\pi }}{7};x = \dfrac{{5\pi }}{{42}} + k\dfrac{{2\pi }}{7}\left( {k \in Z} \right)}$
$2)x = k\pi \left( {k \in Z} \right)$
$\begin{array}{l} 1)\sin 5x + \sin 9x + 2{\sin ^2}x – 1 = 0\\ \Leftrightarrow \sin 5x + \sin 9x – \cos 2x = 0\\ \Leftrightarrow 2\sin 7x\cos 2x – \cos 2x = 0\\ \Leftrightarrow \cos 2x\left( {2\sin 7x – 1} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} \cos 2x = 0\\ 2\sin 7x – 1 = 0 \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} \cos 2x = 0\\ \sin 7x = \dfrac{1}{2} \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} 2x = \dfrac{\pi }{2} + k\pi \\ 7x = \dfrac{\pi }{6} + k2\pi \\ 7x = \dfrac{{5\pi }}{6} + k2\pi \end{array} \right.\left( {k \in Z} \right)\\ \Leftrightarrow \left[ \begin{array}{l} x = \dfrac{\pi }{4} + k\dfrac{\pi }{2}\\ x = \dfrac{\pi }{{42}} + k\dfrac{{2\pi }}{7}\\ x = \dfrac{{5\pi }}{{42}} + k\dfrac{{2\pi }}{7} \end{array} \right.\left( {k \in Z} \right)\\ 2)4\sin 2x – 3\cos 2x = 3\left( {4\sin x – 1} \right)\\ \Leftrightarrow 4\sin 2x – 3\cos 2x – 12\sin x + 3 = 0\\ \Leftrightarrow 8\sin x\cos x – 12\sin x + 3\left( {1 – \cos 2x} \right) = 0\\ \Leftrightarrow 8\sin x\cos x – 12\sin x + 3.2{\sin ^2}x = 0\\ \Leftrightarrow 2\sin x\left( {4\cos x + 3\sin x – 6} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} \sin x = 0\\ 4\cos x + 3\sin x – 6 = 0 \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = k\pi \\ \dfrac{3}{5}\sin x + \dfrac{4}{5}\cos x = \dfrac{6}{5} \end{array} \right.\left( {k \in Z} \right)\\ \Leftrightarrow \left[ \begin{array}{l} x = k\pi \\ \cos \left( {x – \alpha } \right) = \dfrac{6}{5}(vn)\left( {\alpha :\cos \alpha = \dfrac{4}{5};\sin \alpha = \dfrac{3}{5}} \right) \end{array} \right.\left( {k \in Z} \right)\\ \Leftrightarrow x = k\pi \left( {k \in Z} \right) \end{array}$