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

## Toán Lớp 11: 1) Sinx + Sin2x + Sin3x =0 2) Sinx + Sin2x + Sin3x + Sin4x =0 3) Sin ²x + sin ² 3x = Cos ² 2x + Cos ² 4x mn ơi giúp em với em cảm ơn

Toán Lớp 11: 1) Sinx + Sin2x + Sin3x =0
2) Sinx + Sin2x + Sin3x + Sin4x =0
3) Sin ²x + sin ² 3x = Cos ² 2x + Cos ² 4x
mn ơi giúp em với
em cảm ơn

1. 1.
$\sin x+\sin3x+\sin2x=0$
$\to 2\sin2x.\cos x+\sin2x=0$
$\to \sin2x(2\cos x+1)=0$
$\to \left[ \begin{array}{l} \sin2x=0\\ \cos x=\dfrac{-1}{2}\end{array} \right.$
$\to \left[ \begin{array}{l}x=\dfrac{k\pi}{2}\\ x=\pm\dfrac{2\pi}{3}+k2\pi\end{array} \right.$
2.
$\sin x+\sin4x+\sin2x+\sin3x=0$
$\to 2\sin\dfrac{5x}{2}\cos\dfrac{3x}{2}+2\sin\dfrac{5x}{2}\sin\dfrac{x}{2}=0$
$\to 2\sin\dfrac{5x}{2}\left( \cos\dfrac{3x}{2}+\cos\dfrac{x}{2}\right)=0$
$\to 2\sin\dfrac{5x}{2}.2\cos x.\cos\dfrac{x}{2}=0$
$\to \left[\begin{array}{l} \sin x=\dfrac{5x}{2}\\ \cos x=0\\ \cos\dfrac{x}{2}=0\end{array}\right.$
$\to \left[\begin{array}{l} x=\dfrac{k2\pi}{5}\\ x=\dfrac{\pi}{2}+k\pi\\ x=\pi+k2\pi \end{array}\right.$
3.
$\sin^2x+\sin^23x=\cos^22x+\cos^24x$
$\to \dfrac{1-\cos2x+1-\cos6x}{2}=\dfrac{1+\cos4x+1+\cos8x}{2}$
$\to \cos2x+\cos8x+\cos4x+\cos6x=0$
$\to 2\cos5x.\cos3x+2\cos5x.\cos x=0$
$\to 2\cos5x(\cos3x+\cos x)=0$
$\to 2\cos5x.2\cos2x.\cos x=0$
$\to \left[\begin{array}{l} \cos5x=0 \\ \cos2x=0 \\ \cos x=0\\ \end{array}\right.$
$\to \left[\begin{array}{I} x=\dfrac{\pi}{10}+\dfrac{k\pi}{5}\\ x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\ x=\dfrac{\pi}{2}+k\pi \end{array}\right.$

2. Đáp án:

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