1. cos+ctg/1+sin= 2. cos^2/1+tg^2 - sin^2/1+ctg^2=

Решение:

1. (cos+ctg)/(1 + sin) = (cos+cosa/sina)/(1 + sin) =

(sina * cos/sina + cosa/sina)/(1 + sin) =

((sina * cos + cosa)/sina)/(1 + sin) =

(cos * (sina +1)/sina)/(1 + sin) =

(cos * (sina +1))/(sina * (1 + sin) = cosa/sina = ctga;

2. Есть формулы 1 + tg^2 = 1/cos^2 и 1 + ctg^2 = 1/sin^2:

cos^2/(1 + tg^2) - sin^2/(1 + ctg^2) =

cos^2/(1/cos^2) - sin^2/(1/sin^2) =

cos^4 - sin^4 = (cos^2 - sin^2) * (cos^2 + sin^2) = cos^2 (2*a).

Ответ: 1) ctga; 2) cos^2 (2*a).