To simplify this expression, we can use trigonometric identities to manipulate the terms.

Recall the following trigonometric identities:

sin(90 + θ) = cosθcos(180 + θ) = -cosθcos2θ = cos^2θ - sin^2θtanθ = sinθ/cosθ

Using these identities, we can simplify the expression step by step:

sin(90 + a) = cos(a)
cos(180 + a) = -cos(a)
cos2(a) = cos^2(a) - sin^2(a)
tan(a) = sin(a)/cos(a)

Let's simplify the expression:

cos(a) (-cos(a)) / [cos^2(a) - sin^2(a)] (sin(a) / cos(a))

= -cos(a)^2 / [cos^2(a) - sin^2(a)] * sin(a) / cos(a)

= -cos(a)^2 / [cos^2(a) - (1 - cos^2(a))] * sin(a) / cos(a)

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

= -cos(a)^2 / [2cos^2(a) - 1] * sin(a) / cos(a)

= -cos(a) * sin(a) / [2cos^2(a) - 1]

= -sin(2a) / [2cos^2(a) - 1]

Therefore, the simplified expression is -sin(2a) / [2cos^2(a) - 1].