43. Demostrar las siguientes identidades trigonométricas:

a) ((2sin^2 (theta) - 1) ^ 2)/(sin^4 (theta) - cos^4 (theta)) = 1 - 2cos^2 (theta)

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

c) tan(alpha) + 1/(cos^3 (alpha)) - 1/(sin(alpha) - tan(alpha)) = (sin^2 (alpha))/(cos^3 (alpha))

d) (3cos^2 (z) + 5sin(z) - 5)/(cos^2 (z)) = (3sin(z) - 2)/(1 + sin(z))

e) (2sin^2 (omega) + 3cos(omega) - 3)/(sin^2 (omega)) = (2cos(omega) - 1)/(1 + cos(omega))

f) (sin^2 (t) + 4sin(t) + 3)/(cos^2 (t)) = (3 + sin(t))/(1 - sin(t))

g) sec(y) - (cos(y))/(1 + sin(y)) = tan(y)