Our expression is 1 + 2sin(a)cos(a) + cos(2a) - sin(2a).

Using trigonometric identities, we can simplify this expression as follows:

cos(2a) = cos^2(a) - sin^2(a)
sin(2a) = 2sin(a)cos(a)

Now substitute these identities into our expression:

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

Now combine like terms:

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

Using the Pythagorean identity cos^2(a) + sin^2(a) = 1:

1 + 1 - sin^2(a)

Combine terms again:

2 - sin^2(a)

Therefore, the simplified expression is 2 - sin^2(a).