\(cosx=sin\frac{\pi}{3}\)
\(\Leftrightarrow cosx=cos\left(\frac{\pi}{2}-\frac{\pi}{3}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{3}+k2\pi\\x=-\frac{\pi}{3}+k2\pi\end{matrix}\right.\)
cosx=sinπ3cosx=sinπ3
⇔cosx=cos(π2−π3)⇔cosx=cos(π2−π3)
⇔[x=π3+k2πx=−π3+k2π
\(\Leftrightarrow cosx=cos\left(\frac{\pi}{6}\right)\)
\(\Rightarrow x=\pm\frac{\pi}{6}+k2\pi\)