$cos\Bigg(2x+\dfrac{3\pi}{4}\Bigg)=sin\Bigg(\dfrac{\pi}{2}+x\Bigg)$
$↔ cos\Bigg(2x+\dfrac{3\pi}{4}\Bigg)=cosx$
$↔ \left[ \begin{array}{l}2x+\dfrac{3\pi}{4}=x+k2\pi\\2x+\dfrac{3\pi}{4}=-x+k2\pi\end{array} \right.$
$↔ \left[ \begin{array}{l}x=-\dfrac{3\pi}{4}+k2\pi\\x=-\dfrac{\pi}{4}+\dfrac{k2\pi}{3}\end{array} \right.$ $(k∈Z)$