Let's simplify the given expression step by step:

First, rewrite the expression as follows:

(tan^2a / (1 + tan^2a + cos^2a)) * cos^2a

Note that tan^2a = sin^2a / cos^2a. Therefore, we can rewrite the expression as:

(sin^2a / cos^2a) / (1 + sin^2a / cos^2a + cos^2a) * cos^2a

To simplify further, let's find a common denominator for the terms in the denominator:

(sin^2a / cos^2a) / ((cos^2a + sin^2a) / cos^2a) * cos^2a

Now, simplify the expression:

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

(sin^2a / cos^2a) * cos^2a

sin^2a

Therefore, the simplified expression is sin^2a.