For the life of me, I can't prove this. Please show your steps, and thank you so much for the help.

(secx - tanx)^2 + 1 = 2tanx
csc(secx-tanx)

I assume what you mean is this:


\frac {(sec(x)-tan(x))^2 + 1}{csc(x)(sec(x)- tan(x))} = 2 tan(x)


as usual with this type of identity proof, convert all the secant, cosecant and tangent functions to their sine and cosine equivalents, then simplify the resulting fractions. Along the way you will have to apply the identity sin^2x + cos^2x = 1. Try it and show us how far you get, then we can help if you get stuck.