tan(x+pi/2)=1
\(\Leftrightarrow x+\dfrac{\Pi}{2}=\dfrac{\Pi}{4}+k\Pi\)
\(\Leftrightarrow x=-\dfrac{\Pi}{4}+k\Pi\)
\(sin\left(2x-\dfrac{\Pi}{6}\right)=sin\left(-\dfrac{\Pi}{2}+2k\Pi-\dfrac{\Pi}{6}\right)\)
\(=sin\left(k2\Pi-\dfrac{2}{3}\Pi\right)=sin\left(-\dfrac{2}{3}\Pi\right)=-\dfrac{\sqrt{3}}{2}\)