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

Toán Lớp 11: Giải pt sau a) cosx – √3 sinx = √2 b) sin2x – cos2x = √2 Mn giúp mk vs ạ , mk camon

Toán Lớp 11: Giải pt sau
a) cosx – √3 sinx = √2
b) sin2x – cos2x = √2
Mn giúp mk vs ạ , mk camon

Comments ( 2 )

  1. $a)cosx-\sqrt{3}sinx=\sqrt{2}$
    $⇔2cos\bigg(x+\dfrac{π}{3}\bigg)=\sqrt{2}$
    $⇔cos\bigg(x+\dfrac{π}{3}\bigg)=\dfrac{\sqrt{2}}{2}$
    $⇔$\(\left[ \begin{array}{l}x+\dfrac{π}{3}=\dfrac{π}{4}+k2π\\x+\dfrac{π}{3}=-\dfrac{π}{4}+k2π\end{array} \right.\) 
    $⇔$\(\left[ \begin{array}{l}x=-\dfrac{π}{12}+k2π\\x=-\dfrac{7π}{12}+k2π\end{array} \right.\) 
    $(k\in\mathbb{Z})$
    $b)sin2x-cos2x=\sqrt{2}$
    $⇔\sqrt{2}sin\bigg(2x-\dfrac{π}{4}\bigg)=\sqrt{2}$
    $⇔sin\bigg(2x-\dfrac{π}{4}\bigg)=1$
    $⇔2x-\dfrac{π}{4}=\dfrac{π}{2}+k2π$
    $⇔x=\dfrac{3π}{8}+kπ$
    $(k\in\mathbb{Z})$

  2. Đáp án:
     
    Giải thích các bước giải:
     

    toan-lop-11-giai-pt-sau-a-cos-3-sin-2-b-sin2-cos2-2-mn-giup-mk-vs-a-mk-camon

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