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