To simplify the given expression, we can start by using the trigonometric identity:

1 - cos^2(α) = sin^2(α)

Next, we can rewrite the expression as:

(1 - cos^2(α))(1 + tan^2(α))

Substitute sin^2(α) for 1 - cos^2(α):

(sin^2(α))(1 + tan^2(α))

Now, recall that tan(α) = sin(α) / cos(α), so tan^2(α) = sin^2(α) / cos^2(α)

Therefore, our expression becomes:

sin^2(α)(1 + sin^2(α) / cos^2(α))

Now, expand the expression:

sin^2(α) + sin^4(α) / cos^2(α)

Our simplified expression is:

sin^2(α) + sin^4(α) / cos^2(α)