I'm having difficulties simplifying the expression.
$\displaystyle
cos(\frac{pi}2-x)csc(-x)
$
Remember that $\displaystyle \cos \bigg(\frac{\pi}{2} - \theta\bigg) = \sin(\theta) $
And $\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)} $
Hence:
$\displaystyle \cos \bigg(\frac{\pi}{2} - x \bigg) \csc(-x) = \sin(x) \frac{1}{\sin(-x)} = \sin(x) \frac{1}{-\sin(x)} = \frac{\sin(x)}{-\sin(x)} = -1 $
Note that $\displaystyle \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b) $ and
$\displaystyle csc(x) =\frac{1}{\sin(x)}$ and that
$\displaystyle \sin(-x)=-\sin(x)$ sine is an odd function
$\displaystyle \cos\left( \frac{\pi}{2}-x\right)\csc(-x)=\frac{\cos\left( \frac{\pi}{2}-x\right)}{\sin(-x)}= $
$\displaystyle \frac{\cos(\frac{\pi}{2})\cos(x)+\sin(\frac{\pi}{2 })\sin(x) }{-\sin(x)}= \frac{\sin(x)}{-\sin(x)}=-1$