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4sin^x + 4cosx -1 =0

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4sin^x + 4cosx -1 =0

in progress 0 Môn Toán Kiệt Gia 4 years 2020-10-31T13:23:08+00:00 2 Answers 312 views 0
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  1. Sapo1 Sapo1 0 2020-10-31T13:24:27+00:00 October 31, 2020 at 1:24 pm Reply

    `4sin² x + 4cosx – 1 = 0`

    `<=> 4(1 – cos² x) + 4cos x – 1 = 0`

    `<=> 4 – 4cos² x + 4cos x – 1 = 0`

    `<=>` \(\left[ \begin{array}{l}cos x = \dfrac{3}{2} (l)\\cos x = -\dfrac{1}{2}\end{array} \right.\)

    `=> cos x = -1/2`

    `<=> x = ±(2π)/3 + k2π` `(k ∈ ZZ)`

  2. Maris Maris 0 2020-10-31T13:25:04+00:00 October 31, 2020 at 1:25 pm Reply

    $4\sin^2x+4\cos x-1=0$

    $\Leftrightarrow 4-4\cos^2x+4\cos x-1=0$

    $\Leftrightarrow -4\cos^2x+4\cos x +3=0$

    $\Leftrightarrow \cos x=1,5$ (loại), $\cos x=-0,5$ (TM)

    $\cos x=-0,5\Leftrightarrow x=\pm\dfrac{2\pi}{3}+k2\pi$

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