Giải phương trình : Sin^2x + sin^23x= cos^22x + cos^24x

Question

Giải phương trình :
Sin^2x + sin^23x= cos^22x + cos^24x

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Reagan 5 tháng 2021-07-18T14:42:52+00:00 1 Answers 81 views 0

Answers ( )

  1. tuminh2
    0
    2021-07-18T14:43:54+00:00
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    $\Leftrightarrow \dfrac{1-\cos2x+1-\cos6x}{2}=\dfrac{1+\cos4x+1+\cos8x}{2}$

    $\Leftrightarrow \cos2x+\cos8x+\cos4x+\cos6x=0$

    $\Leftrightarrow 2\cos5x.\cos3x+2\cos5x.\cos x=0$

    $\Leftrightarrow 2\cos5x(\cos3x+\cos x)=0$

    $\Leftrightarrow 4\cos5x.\cos2x.\cos x=0$

    $+) \cos5x=0\Leftrightarrow x=\dfrac{\pi}{10}+\dfrac{k\pi}{5}$

    $+) \cos2x=0\Leftrightarrow x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}$

    $+) \cos x=0\Leftrightarrow x=\dfrac{\pi}{2}+k\pi$

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