Let's simplify the left side of the equation:

tg^2alpha - sin^2alpha

Using the trigonometric identities:

tan^2(alpha) = sec^2(alpha) - 1sin^2(alpha) + cos^2(alpha) = 1

We can rewrite the left side as:

sec^2(alpha) - 1 - sin^2(alpha)

Now, substituting sin^2(alpha) = 1 - cos^2(alpha) into the equation:

sec^2(alpha) - 1 - (1 - cos^2(alpha))

Simplifying further, we get:

sec^2(alpha) - 1 - 1 + cos^2(alpha)

sec^2(alpha) + cos^2(alpha) - 2

Using the trigonometric identity cos^2(alpha) = 1 - sin^2(alpha):

sec^2(alpha) + 1 - sin^2(alpha) - 2

sec^2(alpha) - sin^2(alpha) - 1

Now, our expression becomes:

tg^2(alpha) - sin^2(alpha) = sec^2(alpha) - sin^2(alpha) - 1

I hope this helps. Let me know if you need further assistance.