4sin^23x+2( căn 3+1)cos3x-căn 3=4 giúp mình với ạ

Question

4sin^23x+2( căn 3+1)cos3x-căn 3=4
giúp mình với ạ

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Bella 4 tháng 2021-08-11T23:18:02+00:00 2 Answers 349 views 0

Answers ( )

    0
    2021-08-11T23:19:21+00:00

    Đáp án:

    $\left[\begin{array}{l}x=\pm\dfrac{\pi}{9}+k\dfrac{2\pi}{3}\\x = \pm\dfrac{\pi}{18}+k\dfrac{2\pi}{3}\end{array}\right.\quad(k \in \Bbb Z)$

    Giải thích các bước giải:

    $\begin{array}{l}4\sin^23x+2(\sqrt3+1)\cos3x-\sqrt3=4\\ \Leftrightarrow 4(1 – \cos^23x) + 2(\sqrt3+1)\cos3x-\sqrt3=4\\ \Leftrightarrow -4\cos^23x + 2(\sqrt3+1)\cos3x – \sqrt3 = 0\\ \Leftrightarrow \left[\begin{array}{l}\cos3x=\dfrac{1}{2}\\\cos3x = \dfrac{\sqrt3}{2}\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}3x=\pm\dfrac{\pi}{3}+k2\pi\\3x = \pm\dfrac{\pi}{6}+k2\pi\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x=\pm\dfrac{\pi}{9}+k\dfrac{2\pi}{3}\\x = \pm\dfrac{\pi}{18}+k\dfrac{2\pi}{3}\end{array}\right.&(k \in \Bbb Z)\end{array}$

    -1
    2021-08-11T23:19:34+00:00

        4sin²3x+2(√3 + 1)cos3x-√3=4

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