pt: sin 3x + sin 5x + sin 7x = 0

Đáp án + Giải thích các bước giải:

`~rai~`

\(\sin3x+\sin5x+\sin7x=0\\\Leftrightarrow (\sin3x+\sin7x)+\sin5x=0\\\Leftrightarrow 2\sin5x\cos2x+\sin5x=0\\\Leftrightarrow \sin5x(2\cos2x+1)=0\\\Leftrightarrow \left[\begin{array}{I}\sin5x=0\\\cos2x=-\dfrac{1}{2}\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}5x=k\pi\\2x=\pm\dfrac{2\pi}{3}+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=k\dfrac{\pi}{5}\\x=\pm\dfrac{\pi}{3}+k\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Vậy S=}\left\{k\dfrac{\pi}{5};\pm\dfrac{\pi}{3}+k\pi\Big|k\in\mathbb{Z}\right\}.\)