Answer
The trigonometric Identity is verified.
$sin~t~csc(\frac{\pi}{2}-t)=tan~t$
Work Step by Step
We know that:
$csc(\frac{\pi}{2}-t)=sec~t~~$ (Cofunction Identity, page 508)
$sec~t=\frac{1}{cos~t}$
Start at the left side of the equation:
$sin~t~csc(\frac{\pi}{2}-t)=sin~t~sec~t=sin~t~\frac{1}{cos~t}=\frac{sin~t}{cos~t}=tan~t$
