Answer
The identity is verified.
$cot(\frac{\pi}{2}-x)~csc~x=sec~x$
Work Step by Step
$cot(\frac{\pi}{2}-x)=tan~x$
$csc~x=\frac{1}{sin~x}$
$sec~x=\frac{1}{cos~x}$
$cot(\frac{\pi}{2}-x)~csc~x=tan~x~\frac{1}{sin~x}=\frac{sin~x}{cos~x}~\frac{1}{sin~x}=\frac{1}{cos~x}=sec~x$
