Question

GPT: \(2\sin2x-\sqrt{2}=0\)

Answer 1

\(\Leftrightarrow2\sin2x=\sqrt{2}\)

\(\Leftrightarrow\sin2x=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow\sin2x=\dfrac{\pi}{4}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{\pi}{4}+k2\pi\\2x=\pi-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{8}+k\pi\\x=\dfrac{3\pi}{8}+k\pi\end{matrix}\right.\left(k\in Z\right)\)

Answer 2

it's not me OoO