To prove the given equation tg^2x - sin^2x = tg^2x * sin^2x, we can simplify each side separately.

Starting with the left side tg^2x - sin^2x:

Using the trigonometric identity tg^2x = sin^2x / cos^2x, we can rewrite the left side as:

sin^2x / cos^2x - sin^2x

Next, we can combine the fractions on the left side:

(sin^2x - sin^2x * cos^2x) / cos^2x

Since sin^2x = 1 - cos^2x, we can substitute in the above expression:

((1 - cos^2x) - (1 - cos^2x) * cos^2x) / cos^2x
((1 - cos^2x) - (cos^2x - cos^4x)) / cos^2x
(1 - cos^2x - cos^2x + cos^4x) / cos^2x
(1 - 2cos^2x + cos^4x) / cos^2x

Now we can expand and simplify the expression:

1/cos^2x - 2 - 1 + cos^2x
1/cos^2x - 3 + cos^2x

This is not equal to the right side tg^2x * sin^2x unless there is a typo in the original equation, or it was derived incorrectly.