To simplify this expression, use the trigonometric identity:
cos^2(a) - sin^2(a) = cos(2a)

Therefore, the expression becomes:
(cos(2a) - 4sin^2(a)) / 2cos^2(a)

Next, factor out sin^2(a) from the numerator:
= (cos(2a) - 4sin^2(a)) / 2cos^2(a)
= cos(2a)/ 2cos^2(a) - 4sin^2(a) / 2cos^2(a)
= ((cos(2a)/ 2cos^2(a)) - 2sin^2(a) / cos^2(a))
= (1/2 - 2tan^2(a))

Therefore, the simplified expression is: 1/2 - 2tan^2(a)