Please help me verify this identity? sect - cost/sect = sin²t

Remember these identities.
sect = 1/cost
sin²t = 1 - cos²t

= (sect - cost) / sect
= sect/sect - cost/sect
= 1 - cost(cost)
= 1 - cos²t
= sin²t (Verified)

Have a good day.

..sec(t) - cos(t)
--------------------------
........sec(t)

recall sec(t) = 1/cos(t)

....1
----------- - cos(t)
...cos(t)...................cos(t)
=---------------------- x -------------
.........1....................cos(t)
-----------------
....cos(t)

.....1-cos^2(t)
= -------------------
..........1

recall sin^2(t) + cos^2(x) = 1
sin^2(t) = 1- cos^2(t)


= sin^2(t) prove//

(sect - cost) / sect = (1/cost) - cost / (1/cost)

= 1 - cos^2t = sin^2t