Question

Giải các phương trình sau:

\(\text{sin}\left(x+\dfrac{\pi}{7}\right)+sin\left(\dfrac{3\pi}{2}-\dfrac{\pi}{5}\right)=0\)

Answer 1

\(\sin\left(x+\dfrac{\pi}{7}\right)+\sin\left(\dfrac{3\pi}{2}-\dfrac{\pi}{5}\right)=0\\ \Rightarrow\sin\left(x+\dfrac{\pi}{7}\right)+\sin\left(\dfrac{13\pi}{10}\right)=0\\ \Rightarrow\sin\left(x+\dfrac{\pi}{7}\right)=-\sin\left(\dfrac{13\pi}{10}\right)=sin\left(-\dfrac{13\pi}{10}\right)\\ \Rightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{7}=-\dfrac{13\pi}{10}+k2\pi\\x+\dfrac{\pi}{7}=\pi+\dfrac{13\pi}{10}+k2\pi\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{101\pi}{70}+k2\pi\\x=\dfrac{151\pi}{70}+k2\pi\end{matrix}\right.\)