sin^4(cos^3(3x)) + cos^4(cos^3 (3x)) =1
Найдите все x на промежутке [0;1]
99 балов

sin^2(cos^3(3x)) = t, 0 <= t <= sin^2(1) < 1cos^2(cos^3(3x)) = 1 - tt^2 + (1-t)^2 = 1t^2 + t^2 - 2t + 1 = 1t(t - 1) = 0t = 1 - не подходитt = 0sin(cos^3(3x)) = 0cos^3(3x) = y, |y| <= 1sin(y) = 0y = Пk, П > 1 -> y = 0cos^3(3x) = 0cos(3x) = 03x = П/2 + Пkx = П/6 + Пk/30 <= x <= 10 < П/6 < 1П/3 > 1x = П/6 - единственное решение на [0;1]