Если tg x/2 = 1/2, то sin⁴x-cos⁴x =

sin^4 (X) - cos^4 (x) = (sin^2 (x) - cos^2 (X)) * (sin^2 (x) + cos^2 (x)) = sin^2 (x) - cos^2 (x) ; sin^2 (x) - cos^2 (x) = (2tg (x/2) / (1+tg^2 (x/2))) ^2 - ((1-tg^2 (x/2)) / (1+tg^2 (x/2))) ^2;

подставляем и получаем результат 7/25