verify identity:

tanx=cscx-cotx

RS = 1/sinx - cosx/sinx

= (1- cosx)/sinx
≠ tanx

this is not an identity,
let x = 45°
tan45 = 1
csc45 - cot45 = √2 - 1 ≠ 1

all we needde was one counterexample to show it to be false.