Help with verifying trig identities

Secx over sinx - sinx over cosx= cotx

secx/sinx - sinx/cosx
=1/cosxsinx - sin^2 x /cosxsinx
=(1-sin^2 x)/cosxsinx
=cos^2 x /cosxsinx
=cosx/sinx
=1/tanx
=cotx

sec(x)/sin(x) - sin(x)/cos(x) =>
(sec(x) * cos(x) - sin(x) * sin(x)) / (sin(x)cos(x)) =>
(1 - sin(x)^2) / (sin(x)cos(x)) =>
cos(x)^2 / (sin(x)cos(x)) =>
cos(x)/sin(x) =>
cot(x)

SOH CAH TOA

sin: opposite/hypotenuse
Cos: adjacent/hypotenuse
Tan: opposite/adjacent