Sinx+cosx=2√2 sinxcosx

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Sinx+cosx=2√2 sinxcosx

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Khang Minh 4 years 2020-10-29T15:18:57+00:00 1 Answers 131 views 0

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  1. Nho
    0
    2020-10-29T15:20:19+00:00
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    Đáp án:

    $\left[\begin{array}{l}x =  \dfrac{\pi}{4}+ k\pi\\x = \dfrac{\pi}{4} + k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in\Bbb Z)$

    Giải thích các bước giải:

    $\sin x + \cos x = 2\sqrt2\sin x\cos x$

    $\Leftrightarrow \sqrt2\sin\left(x + \dfrac{\pi}{4}\right) = \sqrt2\sin2x$

    $\Leftrightarrow \sin\left(x + \dfrac{\pi}{4}\right) = \sin2x$

    $\Leftrightarrow \left[\begin{array}{l}x + \dfrac{\pi}{4} = 2x + k\pi\\x + \dfrac{\pi}{4} = \pi – 2x + k2\pi\end{array}\right.$

    $\Leftrightarrow \left[\begin{array}{l}x =  \dfrac{\pi}{4}+ k\pi\\x = \dfrac{\pi}{4} + k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in\Bbb Z)$

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )