[1-sin^2(alfa+beta)]/cos^2(alfa+beta)

[1-sin^2(alfa+beta)]/cos^2(alfa+beta)

= cos^2(alfa+beta) / cos^2(alfa+beta)
= 1

(remember .... 1 - sin^2 x = cos^2 x)

remember that 1=sin^2 Theta + cos^2 Theta, so

1-sin^2 Theta=cos^2 theta

To simplify the expression [1-sin^2(alfa+beta)]/cos^2(alfa+beta), we can first use the Pythagorean identity sin^2(alfa+beta) + cos^2(alfa+beta) = 1 to rewrite the numerator:

1 - sin^2(alfa+beta) = cos^2(alfa+beta).

Now, substituting this into the expression, we have:

cos^2(alfa+beta)/cos^2(alfa+beta).

Since the numerator and denominator are the same, the expression simplifies to:

1.

Therefore, the final simplified expression is 1.