Question

how to verify the identities,
cot x -1/ 1-tan x = cot x

Answer 1

do some algebra. my best advice is to write everything in terms of sine and cosine, then replace cosine by "a" and sine by "b" and see what the algebra brings. in other words start with
\[\frac{\frac{a}{b}-1}{1-\frac{b}{a}}\] and then see if you can turn it in to
\[\frac{a}{b}\] you may need a trig identity along the way, but you should simplify the compound fraction first

Answer 2

oh in fact you need no trig at all. the expression on the left "simplifies" to the one on the right. so this has absolutely nothing to do with trig at all.
never could tell my left from my right