sin(pi+pi/6)=cos(pi/3-2x) ai giúp em với ạ!

Question

sin(pi+pi/6)=cos(pi/3-2x) ai giúp em với ạ!

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Katherine 3 tháng 2021-07-19T09:17:48+00:00 1 Answers 4 views 0

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    2021-07-19T09:18:58+00:00

    Đáp án:

    $\begin{array}{l}
    \sin \left( {x + \dfrac{\pi }{6}} \right) = \cos \left( {\dfrac{\pi }{3} – 2x} \right)\\
     \Rightarrow \sin \left( {x + \dfrac{\pi }{6}} \right) = \sin \left( {\dfrac{\pi }{2} – \dfrac{\pi }{3} + 2x} \right)\\
     \Rightarrow \left[ \begin{array}{l}
    x + \dfrac{\pi }{6} = \dfrac{\pi }{2} – \dfrac{\pi }{3} + 2x + k2\pi \\
    x + \dfrac{\pi }{6} = \pi  – \left( {\dfrac{\pi }{2} – \dfrac{\pi }{3} + 2x} \right) + k2\pi 
    \end{array} \right.\\
     \Rightarrow \left[ \begin{array}{l}
    x =  – k2\pi \\
    3x = \dfrac{{2\pi }}{3} + k2\pi 
    \end{array} \right.\\
     \Rightarrow \left[ \begin{array}{l}
    x = k2\pi \\
    x = \dfrac{{2\pi }}{9} + \dfrac{{k2\pi }}{3}
    \end{array} \right.
    \end{array}$

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