(sec x - tan x) (sec x - tan x) + 1
------------------------------------------------- = 2 tan x
sec x . Cosec x - tan x . Cosec x

As usual with these types of proofs - first convert the tan, sec and csc functions to their sine and cosine equivalents, then look for ways to simplify the resulting messy fraction and where possible apply other simplifying identities, such as sin^2 + cos^2 = 1.