1) (1+tg²alpha) cos²alpha 2) tg alpha + tg beta дробь ctg alpha + ctg beta 3) cos² alpha - ctg² alpha дробь sin² alpha - tg² alpha

1. Раскроем скобки и упростим выражение:

(1 + tg^2 (α)) cos^2 (α) = cos^2 (α) + tg^2 (α) cos^2 (α) = cos^2 (α) + sin^2 (α) = 1.

2. Z = (tg (α) + tg (β)) / (ctg (α) + ctg (β));

Z = {sin (α) / cos (α) + sin (β) / cos (β) }/{cos (α) / sin (α) + cos (β) / sin (β) };

Z = { (sin (α) cos (β) + cos (α) sin (β)) / (cos (α) cos (β)) }/{ (cos (α) sin (β) + sin (α) cos (β)) / (sin (α) sin (β)) };

Z = {sin (α + β) / (cos (α) cos (β)) }/{sin (α + β) / (sin (α) sin (β)) };

Z = (sin (α) sin (β)) / (cos (α) cos (β));

Z = tg (α) tg (β).

3. Z = (cos^2 (α) - ctg^2 (α)) / (sin^2 (α) - tg^2 (α));

Z = (cos^2 (α) - cos^2 (α) / sin^2 (α)) / (sin^2 (α) - sin^2 (α) / cos^2 (α));

Z = cos^2 (α) / sin^2 (α) * (1 - 1/sin^2 (α)) / (1 - 1/cos^2 (α));

Z = cos^2 (α) / sin^2 (α) * ((sin^2 (α) - 1) / sin^2 (α)) / ((cos^2 (α) - 1) / cos^2 (α));

Z = cos^2 (α) / sin^2 (α) * (-cos^2 (α) / sin^2 (α)) / (-sin^2 (α) / cos^2 (α));

Z = ctg^6 (α).