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