To simplify the expression sin^2 a + tan^2 a * sin^2 a, we can use the trigonometric identity:

tan^2 a = sin^2 a / cos^2 a

Substituting this into the expression, we get:

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

Now, let's simplify further:

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

Using the property of multiplication, we can combine the terms:

sin^2 a + (sin^4 a) / cos^2 a

Now, let's use another trigonometric identity:

cos^2 a = 1 - sin^2 a

Substituting this into the expression, we get:

sin^2 a + (sin^4 a) / (1 - sin^2 a)

Now, let's simplify the expression further:

(sin^2 a * (1 - sin^2 a) + sin^4 a) / (1 - sin^2 a)

Expanding the numerator, we get:

(sin^2 a - sin^4 a + sin^4 a) / (1 - sin^2 a)

Simplifying, we get:

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

Using the identity:

1 - sin^2 a = cos^2 a

We can rewrite the expression as:

sin^2 a / cos^2 a

Finally, using the identity:

tan^2 a = sin^2 a / cos^2 a

We can conclude that the simplified expression is:

tan^2 a