Question

GPT : cos4x . \(\sqrt{\dfrac{\pi^2}{9}^{ }-x^2}\)=0

Answer 1

\(cos4x\cdot\sqrt{\dfrac{\pi^2}{9}-x^2}=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos4x=0\\\sqrt{\dfrac{\pi^2}{9}-x^2}=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}4x=\dfrac{\pi}{2}+k\pi\left(k\in Z\right)\\\dfrac{\pi^2}{9}-x^2=0\end{matrix}\right.\)

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