To simplify the expression, let's rewrite it step by step:

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

= (1-2sin(2a))/cos(a) + sin(a) + 1 - 2cos(2a)/sin(a) - cos(a)

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

= (1 - 4sin(a)cos(a))/cos(a) + sin(a) + 1 - 4cos^2(a) + 2/sin(a) - cos(a)

= (1/cos(a) - 4sin(a))/cos(a) + sin(a) + (1 - 4cos^2(a))/sin(a) - 2cos(a)

= 1 - 4sin^2(a)/cos(a) + sin(a) + 1 - 4cos^2(a)/sin(a) - 2cos(a)

= (1 - 4sin^2(a))/cos(a) + sin(a) + (1 - 4cos^2(a))/sin(a) - 2cos(a)

= cos^2(a) - 4sin^2(a)/cos(a) + sin(a) + sin^2(a) - 4cos^2(a)/sin(a) - 2cos(a)

= cos^3(a) - 4sin^2(a) + sin(a)cos(a) + sin^3(a) - 4cos^3(a) - 2cos^2(a)sin(a)

= cos(a) - 4sin^2(a) + sin(a)cos(a) + sin(a) - 4cos^3(a) - 2cos^2(a)sin(a)

= 2cos(a) - 4sin^2(a) + sin(a)cos(a) - 4cos^3(a) - 2cos^2(a)sin(a)

= 2cos(a) - 4(cos(a))^2 + sin(a)cos(a) - 4(cos(a))^3 - 2(cos(a))^2sin(a)

= 2cos(a) - 4cos^2(a) + sin(a)cos(a) - 4cos^3(a) - 2cos^2(a)sin(a)

= 2cos(a) - 4cos^2(a) + cos(a)sin(a) - 4cos^3(a) - 2cos^2(a)sin(a)

= 2cos(a) - 4cos^2(a) + cos(a)sin(a) - 4cos^3(a) - 2cos^2(a)sin(a)

= 2cos(a)

Therefore, the given expression simplifies to 2cos(a).