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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 11: Sin^6x + Cos^6x = Sin2x giúp mình với mình cảm ơn ạ

Tháng Hai 4, 2023 Toán học 1 Comment 0 views

Toán Lớp 11: Sin^6x + Cos^6x = Sin2x
giúp mình với
mình cảm ơn ạ

Comments ( 1 )

  1. dananhnhu2k4
    dananhnhu2k4
    4 Tháng Hai, 2023 at 4:27 chiều
    Reply
    $\sin^6x+\cos^6x$
    $=(\sin^2x+\cos^2x)(\sin^4x+\cos^4x-\sin^2x\cos^2x)$
    $=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x-\sin^2x\cos^2x$
    $=1-3\sin^2x\cos^2x$
    $=1-\dfrac{3}{4}\sin^22x$
    Phương trình trở thành:
    $1-\dfrac{3}{4}\sin^22x=\sin2x$
    $\to \dfrac{3}{4}\sin^22x+\sin2x-1=0$
    $\to \left[ \begin{array}{l}\sin2x=\dfrac{2}{3}\\\sin2x=-2(\text{loại})\end{array} \right.$
    $\to \left[ \begin{array}{l}2x=\arcsin\dfrac{2}{3}+k2\pi\\2x=\pi-\arcsin\dfrac{2}{3}+k2\pi\end{array} \right.$
    $\to \left[ \begin{array}{l}x=\dfrac{1}{2}\arcsin\dfrac{2}{3}+k\pi\\x=\dfrac{\pi}{2}-\dfrac{1}{2}\arcsin\dfrac{2}{3}+k\pi\end{array} \right.$

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222-9+11+12:2*14+14 = ? ( )

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