Simplify csc(-x)cos(pi/2-x)

$\csc (- x) \cos (\frac{π}{2} - x)$

Since $\csc (- x)$ is an odd function, rewrite $\csc (- x)$ as $- \csc (x)$ .

$- \csc (x) \cos (\frac{π}{2} - x)$

Rewrite $\csc (x)$ in terms of sines and cosines.

$- \frac{1}{\sin (x)} \cos (\frac{π}{2} - x)$

Combine $\cos (\frac{π}{2} - x)$ and $\frac{1}{\sin (x)}$ .

$- \frac{\cos (\frac{π}{2} - x)}{\sin (x)}$

Rewrite $\frac{\cos (\frac{π}{2} - x)}{\sin (x)}$ as a product.

$- (\cos (\frac{π}{2} - x) \frac{1}{\sin (x)})$

Write $\cos (\frac{π}{2} - x)$ as a fraction with denominator $1$ .

$- (\frac{\cos (\frac{π}{2} - x)}{1} \cdot \frac{1}{\sin (x)})$

Simplify.

Divide $\cos (\frac{π}{2} - x)$ by $1$ .

$- (\cos (\frac{π}{2} - x) \frac{1}{\sin (x)})$

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$- (\cos (\frac{π}{2} - x) \csc (x))$

$- \cos (\frac{π}{2} - x) \csc (x)$