To simplify the expression: (sin2a - 2cos a)/(1 + cos2a) - tan a, we can first rewrite sin2a and cos2a in terms of sine and cosine functions.

sin2a = 2sin a cos a
cos2a = 2cos^2 a - 1

Now substitute these values into the expression:

(2sin a cos a - 2cos a)/(1 + 2cos^2 a - 1) - tan a
(2cos a (sin a - 1))/2cos^2 a - tan a
(sin a - 1)/cos a - tan a
(sin a - cos a)/cos a

Therefore, the simplified expression is (sin a - cos a)/cos a.