(sin^2x + tg^2x sin^2x) ctgx = sin^2x (1 + tg^2x) ctgxtg^2x = sin^2x / cos^2xtg^2x = sin^2x / (1 - sin^2x)tg^2x = sin^2x / cos^2x = sin^2x / (1 - sin^2x)
(sin^2x + sin^2x / (1 - sin^2x) sin^2x) ctgx(sin^2x + sin^2x^2 / (1 - sin^2x)) ctgx(sin^2x(1 + sin^2x) / (1 - sin^2x)) ctgx(sin^2x cos^2x / cos^2x) ctgxsin^2x * ctgx
Ответ: sin^2x * ctgx
(sin^2x + tg^2x sin^2x) ctgx = sin^2x (1 + tg^2x) ctgx
tg^2x = sin^2x / cos^2x
tg^2x = sin^2x / (1 - sin^2x)
tg^2x = sin^2x / cos^2x = sin^2x / (1 - sin^2x)
(sin^2x + sin^2x / (1 - sin^2x) sin^2x) ctgx
(sin^2x + sin^2x^2 / (1 - sin^2x)) ctgx
(sin^2x(1 + sin^2x) / (1 - sin^2x)) ctgx
(sin^2x cos^2x / cos^2x) ctgx
sin^2x * ctgx
Ответ: sin^2x * ctgx