\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{2}cos\left(2x-\dfrac{\pi}{2}\right)=\dfrac{1}{2}+\dfrac{1}{2}cos2x\)
\(\Leftrightarrow-sin2x=cos2x\)
\(\Leftrightarrow sin2x+cos2x=0\)
\(\Leftrightarrow\sqrt{2}sin\left(2x+\dfrac{\pi}{4}\right)=0\)
\(\Leftrightarrow2x+\dfrac{\pi}{4}=k\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{8}+\dfrac{k\pi}{2}\)