Chủ đề này có 2 trả lời

[Issac Newton]

Giải pt $sin^22x-sin^23x=0$

[henry0905]

Giải pt $sin^22x-sin^23x=0$

$\Leftrightarrow (sin2x-sin3x)(sin2x+sin3x)=0$

$\Leftrightarrow \begin{bmatrix} 2x=3x+k2\pi & \\ 2x=\pi -3x+k2\pi & \\ 2x=-3x+k2\pi & \\ 2x=\pi +3x+k2\pi & \end{bmatrix}$

$\Leftrightarrow \begin{bmatrix} x=-k2\pi & \\ x=\frac{\pi +k2\pi}{5} & \\ x=\frac{k2\pi}{5} & \\ x=-\pi-k2\pi & \end{bmatrix}$ với $k\in \mathbb{Z}$

[sieumau88]

Giải pt: $sin^2 \ 2x - sin^2 \ 3x = 0$

$\Leftrightarrow sin^2 \ 3x = sin^2 \ 2x $

$\Leftrightarrow \dfrac{1 - cos \ 6x }{2} = \dfrac{1 - cos \ 4x }{2}$

$\Leftrightarrow cos \ 6x = cos \ 4x $

$\Leftrightarrow \left[ \begin{array}{l} 6x = 4x + k2 \pi \\ 6x = \pi - 4x + k2 \pi \end{array} \right.$ $\left ( k \in \mathbb{Z} \right )$

$\Leftrightarrow \left[ \begin{array}{l} x = k \pi \\ x = \dfrac{\pi}{10} + \dfrac{k \pi}{5} \end{array} \right.$ $\left ( k \in \mathbb{Z} \right )$