The expression
\[
\frac{\tan\left(x-\frac{\pi}{2}\right)\cos\left(\frac{3\pi}{2}+x\right)-\sin^2\left(\frac{7\pi}{2}-x\right)}
{\cos\left(x-\frac{\pi}{2}\right)\tan\left(\frac{3\pi}{2}+x\right)}
\]
simplifies to:
Show Hint
For trigonometric expressions involving shifted angles such as
\[
x\pm\frac{\pi}{2},\quad x\pm\frac{3\pi}{2},
\]
always convert them into basic trigonometric functions first.