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

Toán Lớp 11: GPT: 2(cosx + √3sinx)cosx = cosx – √3sinx + 1

Tháng Mười Hai 1, 2022 Toán học 2 Comments 0 views

Toán Lớp 11: GPT:
2(cosx + √3sinx)cosx = cosx – √3sinx + 1

Comments ( 2 )

  1. thanhbinh2k5
    thanhbinh2k5
    1 Tháng Mười Hai, 2022 at 4:44 sáng
    Reply

    Chúc em học tốt
    TODAY YOU ARE VERY NICE
    #senku
    toan-lop-11-gpt-2-cos-3sin-cos-cos-3sin-1

  2. cobelolen
    cobelolen
    1 Tháng Mười Hai, 2022 at 4:43 sáng
    Reply
    Giải đáp:
    $\left[\begin{array}{l}x = \dfrac{2\pi}{3} + k2\pi\\x= k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in \Bbb Z)$
    Lời giải và giải thích chi tiết:
    $2(\cos x +\sqrt3\sin x)\cos x = \cos x – \sqrt3\sin x + 1$
    $\Leftrightarrow 2\cos^2x – 1 + 2\sqrt3\sin x\cos x = \cos x – \sqrt3\sin x$
    $\Leftrightarrow \cos2x + \sqrt3\sin2x = \cos x – \sqrt3\sin x$
    $\Leftrightarrow \dfrac{1}{2}\cos2x + \dfrac{\sqrt3}{2}\sin2x = \dfrac{1}{2}\cos x -\dfrac{\sqrt3}{2}\sin x$
    $\Leftrightarrow \cos\left(2x -\dfrac{\pi}{3}\right) = \cos\left(x +\dfrac{\pi}{3}\right)$
    $\Leftrightarrow \left[\begin{array}{l}2x – \dfrac{\pi}{3} = x + \dfrac{\pi}{3} + k2\pi\\2x – \dfrac{\pi}{3} =- x -\dfrac{\pi}{3} + k2\pi\end{array}\right.$
    $\Leftrightarrow \left[\begin{array}{l}x = \dfrac{2\pi}{3} + k2\pi\\x= k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in \Bbb Z)$

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

Khánh Ly

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