To simplify the expression, we can use trigonometric identities:

cos(3/2p - 2a) = cos(2a - p/2) = cos(2a)cos(p/2) + sin(2a)sin(p/2)tan(p - a) = sin(p - a) / cos(p - a)sin(p/2 + 2a) = sin(p/2)cos(2a) + cos(p/2)sin(2a)

Using these identities, we can rewrite the expression as follows:

cos(3/2p - 2a)tan(p - a) + sin(p/2 + 2a)
= (cos(2a)cos(p/2) + sin(2a)sin(p/2)) * (sin(p - a) / cos(p - a)) + (sin(p/2)cos(2a) + cos(p/2)sin(2a))
= (cos(2a)cos(p/2)sin(p - a) + sin(2a)sin(p/2)sin(p - a) + sin(p/2)cos(2a) + cos(p/2)sin(2a)) / cos(p - a)

This is the simplified form of the expression.