This is probably a basic arithmetic problem but I have the following to validate

1/(sec + tan) = sec - tan

I simplify to

cos/(sin + 1) = (1-sin)/cos

clearing fractions gives some pythagorean statements which are true, but I bet there's some property about fractions that should tell me the above is true, ie

a/(b+1) = (1-b)/a

How does one verify/validate the identity?