Answer
$\tan(\frac{\pi}{2}-u)=\cot u$
Work Step by Step
Start with the left side:
$\tan(\frac{\pi}{2}-u)$
Express tangent as sine divided by cosine:
$=\frac{\sin(\frac{\pi}{2}-u)}{\cos (\frac{\pi}{2}-u)}$
Expand using the subtraction formulas for sine and cosine:
$=\frac{\sin \frac{\pi}{2}\cos u-\cos \frac{\pi}{2}\sin u}{\cos \frac{\pi}{2}\cos u+\sin \frac{\pi}{2}\sin u}$
Evaluate $\sin \frac{\pi}{2}$ and $\cos \frac{\pi}{2}$:
$=\frac{1*\cos u-0*\sin u}{0*\cos u+1*\sin u}$
$=\frac{\cos u}{\sin u}$
$=\cot u$
Since this equals the right side, the identity has been proven.
