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