Question

Trig / Pre Cal/identities Am I on the right path?

Please do not give the answer. Here is the problem

\( \frac{(sin x- cos x)}{cos} = sec x - cos x\)

I am working on the left side and need to prove it equals the right. This is what I have done so far

\( \frac{(sin^2 x - 2(cos x)(sin x)+cos^2 x}{cos} = sec x - cos x\)

Am I going about this the right way because I don't see where to go from here. Thank you.