Answer
$$\cot \left(\frac{\pi}{2}-x\right) =\tan (x) $$
Work Step by Step
We use the know identities to obtain:
\begin{aligned}
\cot \left(\frac{\pi}{2}-x\right)&=\frac{\cos \left(\frac{\pi}{2}-x\right)}{\sin \left(\frac{\pi}{2}-x\right)}\\
&=\frac{\cos \left(\frac{\pi}{2}\right) \cos (x)+\sin \left(\frac{\pi}{2}\right) \sin (x)}{\sin \left(\frac{\pi}{2}\right) \cos (x)-\cos \left(\frac{\pi}{2}\right) \sin (x)}\\
&=\frac{0 \times \cos (x)+1 \times \sin (x)}{1 \times \cos (x)-0 \times \sin (x)}\\
&=\frac{0+\sin (x)}{\cos (x)-0}\\
&=\frac{\sin (x)}{\cos (x)}=\tan (x)
\end{aligned}
