Question

1-sin^2a/cos^2a-(cosa*tg)^2

Answer 1

(1-sin²a)/cos²a-(cosa*tga)² = cos²a/cos²a - sin²a = 1 - sin²a = cos²a

Answer 2

To simplify the expression (1 - sin^2(a))/(cos^2(a) - (cos(a)*tan(a))^2), we can start by factoring the numerator and denominator separately.

1 - sin^2(a) can be written as cos^2(a) using the Pythagorean identity: sin^2(a) + cos^2(a) = 1. Therefore, we can substitute cos^2(a) for 1 - sin^2(a) in the expression.

The denominator, cos^2(a) - (cos(a)*tan(a))^2, can be simplified using the fact that tan(a) = sin(a)/cos(a). Substituting this value, we get:

cos^2(a) - (cos(a)*tan(a))^2 = cos^2(a) - (cos(a)*sin(a)/cos(a))^2 = cos^2(a) - sin^2(a) = cos^2(a) - (1 - cos^2(a)) [using the Pythagorean identity]

Now, let's simplify the expression further:

(1 - sin^2(a))/(cos^2(a) - (cos(a)tan(a))^2 = cos^2(a)/(cos^2(a) - (1 - cos^2(a))) = cos^2(a)/(cos^2(a) - 1 + cos^2(a)) = cos^2(a)/(2cos^2(a) - 1)

Therefore, the simplified expression is cos^2(a)/(2*cos^2(a) - 1).