[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.