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

Toán Lớp 11: Giải phương trình: $cos^{}2x$ + $cos^{}6x$ + $4sin^{2}x$ = $2_{}$

Toán Lớp 11: Giải phương trình: $cos^{}2x$ + $cos^{}6x$ + $4sin^{2}x$ = $2_{}$

Comments ( 2 )

  1. Giải đáp:
    $S=\left\{\dfrac{k\pi}{4}\,\bigg{|}\,k\in\mathbb Z\right\}$
    Lời giải và giải thích chi tiết:
    $\cos2x+\cos6x+4\sin^2x=2$
    $⇔\cos2x+\cos6x+2(2\sin^2x-1)=0$
    $⇔\cos2x+\cos6x-2\cos2x=0$
    $⇔\cos6x-\cos2x=0$
    $⇔\cos6x=\cos2x$
    $⇔\left[ \begin{array}{l}6x=2x+k2\pi\\6x=-2x+k2\pi\end{array} \right.\,\,(k\in\mathbb Z)⇔\left[ \begin{array}{l}4x=k2\pi\\8x=k2\pi\end{array} \right.\,\,(k\in\mathbb Z)$
    $⇔\left[ \begin{array}{l}x=\dfrac{k\pi}{2}\\x=\dfrac{k\pi}{4}\end{array} \right.\,\,(k\in\mathbb Z)⇔x=\dfrac{k\pi}{4}\,\,(k\in\mathbb Z)$
    Vậy $S=\left\{\dfrac{k\pi}{4}\,\bigg{|}\,k\in\mathbb Z\right\}$.

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