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

Toán Lớp 11: giúp em với Sin^2(3x-π/2)=3/4; Cosx+cos2x+cos3x+cos4x=0; Sinx+sin3x+sin5x+sin7x=0; Sin^2 3x-cos^2(x+π/6)=0

Tháng Hai 15, 2023 Toán học 1 Comment 0 views

Toán Lớp 11: giúp em với
Sin^2(3x-π/2)=3/4;
Cosx+cos2x+cos3x+cos4x=0;
Sinx+sin3x+sin5x+sin7x=0;
Sin^2 3x-cos^2(x+π/6)=0

Comments ( 1 )

  1. thienthanh
    thienthanh
    15 Tháng Hai, 2023 at 3:16 sáng
    Reply
    1.
    $\sin ^2 \Big(3x-\dfrac{\pi}{2}\Big)= \dfrac{3}{4}$
    $\Leftrightarrow \dfrac{1-\cos (6x-\pi)}{2}=\dfrac{3}{4}$
    $\Leftrightarrow 1+ \cos (2\pi – 6x)=\dfrac{3}{2}$
    $\Leftrightarrow \cos (2\pi – 6x)=\dfrac{1}{2}$
    $\Leftrightarrow \left[ \begin{array}{l}2\pi – 6x=\dfrac{\pi}{3}+k2\pi\\2\pi – 6x=\dfrac{-\pi}{3}+k2\pi \end{array}\right.$
    $\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{5\pi}{18}-\dfrac{k\pi}{3}\\x=\dfrac{7\pi}{18}-\dfrac{k\pi}{3} \end{array} \right.(k \in \mathbb{Z})$
    2.
    $\cos x + \cos 2x + \cos 3x + \cos 4x =0$
    $\Leftrightarrow ( \cos x + \cos 3x) + (\cos 2x + \cos 4x)=0$
    $\Leftrightarrow \Big( 2 \cos \dfrac{4x}{2}.\cos \dfrac{-2x}{2}\Big)+ \Big( 2\cos \dfrac{6x}{2}.\cos \dfrac{-2x}{2}\Big)=0$
    $\Leftrightarrow 2 \cos (-x). (\cos 2x +\cos 3x) =0$
    $\Leftrightarrow \left[ \begin{array}{l}\cos x=0\\\cos 2x =- \cos 3x \end{array} \right.$
    $\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{\pi}{2}+k\pi\\x=\dfrac{\pi}{3}+\dfrac{k2\pi}{3}\\x=\pi – k2\pi \end{array} \right.(k \in \mathbb{Z})$
    3. 

    toan-lop-11-giup-em-voi-sin-2-3-2-3-4-cos-cos2-cos3-cos4-0-sin-sin3-sin5-sin7-0-sin-2-3-cos-2-6

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

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