Question

Giải pt lượng giác Giúp em với em cảm ơn ạ

Answer 1

10.

\(sin\dfrac{x+\pi}{5}=-\dfrac{1}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x+\pi}{5}=-\dfrac{\pi}{6}+k2\pi\\\dfrac{x+\pi}{5}=\dfrac{7\pi}{6}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{11\pi}{6}+k2\pi\\x=-\dfrac{41\pi}{6}+k2\pi\end{matrix}\right.\)

Answer 2

11.

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

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\pi}{5}=\dfrac{\pi}{5}+x+k2\pi\\2x-\dfrac{\pi}{5}=\dfrac{4\pi}{5}-x+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2\pi}{5}+k2\pi\\x=\dfrac{\pi}{3}+\dfrac{k2\pi}{3}\end{matrix}\right.\)