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