To simplify this expression, we can use the angle sum and difference identities for cosine.

Recall that cos(90° - a) = sin(a) and cos(180° - a) = -cos(a).

So, the given expression becomes:

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

Now, for simplicity, let's change sin(a) to cos(90° - a):

cos^2(90° - a) - 1/(-cos(a))

Since cos(90° - a) = -sin(a), we get:

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

Simplifying further:

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

So, cos^2(90° - a) - 1/(-cos(a)) simplifies to sin^2(a) - 1/(-cos(a)).