1 + tg^2(-a) - 1/sin(0.5π + 2a)

To simplify this expression, we need to first determine the trigonometric values of tg(-a) and sin(0.5π + 2a).

tg(-a):
Since tangent is an odd function, it can be simplified as follows:
tg(-a) = -tg(a)

sin(0.5π + 2a):
Using the sum-to-product formulas, sin(α + β) = sin(α)cos(β) + cos(α)sin(β), we get:
sin(0.5π + 2a) = sin(0.5π)cos(2a) + cos(0.5π)sin(2a)
sin(0.5π + 2a) = 1 cos(2a) + 0 sin(2a)
sin(0.5π + 2a) = cos(2a)

Now plugging these values back into the original expression:

1 + tg^2(-a) - 1/sin(0.5π + 2a)
= 1 + (-tg(a))^2 - 1/cos(2a)
= 1 + tg^2(a) - 1/cos(2a)
= 1 + tg^2(a) - sec(2a)

Therefore, the simplified expression is:
1 + tg^2(a) - sec(2a)