giúp em 4 sinx + 3 cosx=5

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giúp em
4 sinx + 3 cosx=5

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Latifah 4 years 2020-11-25T00:42:21+00:00 2 Answers 56 views 0

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  1. Acacia
    0
    2020-11-25T00:43:56+00:00
    Reply

    Đáp án:

    $\text{x = $\dfrac{\pi}{2}$ – $\alpha$+ k2$\pi$ (K∈ Z)}$

    Giải thích các bước giải:

     $\text{4sinx + 3cosx = 5}$

    ⇔ $\text{$\dfrac{4}{5}$ sinx +$\dfrac{3}{5}$ cosx = 1}$

    Đặt: $\text{$\left \{ {{cosx=\dfrac{4}{5} } \atop {sinx=\dfrac{3}{5}}} \right.$ }$

    ⇒$\text{sinx.cos$\alpha$ + cosx.sin$\alpha$ = 1}$

    ⇒$\text{sin (x + $\alpha$)=1 }$

    ⇒$\text{x+ $\alpha$ = $\dfrac{\pi}{2}$+ k2$\pi$ }$

    ⇒$\text{x = $\dfrac{\pi}{2}$ – $\alpha$+ k2$\pi$ (K∈ Z)}$

  2. Philomena
    0
    2020-11-25T00:44:13+00:00
    Reply

    $4\sin x+3\cos x=5$

    $\Leftrightarrow \dfrac{4}{5}\sin x+\dfrac{3}{5}\cos x=1$

    Đặt $\cos\alpha=\dfrac{4}{5},\sin\alpha=\dfrac{3}{5}$

    $\Rightarrow \sin(x+\alpha)=1$

    $\Leftrightarrow x+\alpha=\dfrac{\pi}{2}+k2\pi$

    $\Leftrightarrow x=-\alpha+\dfrac{\pi}{2}+k2\pi$

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