Sin^4 (x) - cos^4 (x) = 0.5

Найти х

Sin^4 (x) + cos^4 (x) = sin2x-1/2

(sin^2 (x) + cos^2 (x)) ^2 - 2sin^2 (x) cos^2 (x) = sin2x - 1/2

1 - 1/2sin^2 (2x) = sin2x - 1/2

sin^2 (2x) + 2sin2x - 3 = 0;

D/4 = 1 + 3 = 4

sinx = - 1+-2

Подходит только sin x = 1

x = pi/2 + 2k*pi, k = + - 1; +-2 ...