a/ \(\Leftrightarrow\pi.cosx=\frac{\pi}{2}+k2\pi\)
\(\Leftrightarrow cosx=\frac{1}{2}+2k\)
\(-1\le cosx\le1\Rightarrow-1\le\frac{1}{2}+2k\le1\)
\(\Rightarrow k=0\Rightarrow cosx=\frac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{3}+k2\pi\\x=-\frac{\pi}{3}+k2\pi\end{matrix}\right.\)
b/ \(\Leftrightarrow\left[{}\begin{matrix}\frac{\pi}{6}\left(sin\left(x-13+\frac{\pi}{2}\right)\right)=\frac{\pi}{6}+k2\pi\\\frac{\pi}{6}\left(sin\left(x-13+\frac{\pi}{2}\right)\right)=-\frac{\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x-13+\frac{\pi}{2}\right)=1+12k\\sin\left(x-13+\frac{\pi}{2}\right)=-1+12k\end{matrix}\right.\) \(\Rightarrow k=0\)
\(\Rightarrow\left[{}\begin{matrix}sin\left(x-13+\frac{\pi}{2}\right)=1\\sin\left(x-13+\frac{\pi}{2}\right)=-1\end{matrix}\right.\)
\(\Leftrightarrow cos\left(x-13+\frac{\pi}{2}\right)=0\)
\(\Leftrightarrow sin\left(x-13\right)=0\)
\(\Leftrightarrow x-13=k\pi\)
\(\Rightarrow x=13+k\pi\)
