Question

How do you verify the identity `sec^2y-cot^2(pi/2-y)=1`?

Answer 1

Trig unit circle and property of complementary arcs -->
`cot (pi/2 - y) = tan y`
The equation becomes:
#1/(cos^2 y) - sin^2 y/(cos^2 y) = (1 - sin^2 y)/(cos^2 y) = = cos^2 y/(cos^2 y) = 1#