2 * cos(x)^2 + (2 - sqrt(2)) * sin(x) + sqrt(2) - 2 = 0
cos(x)^2 = 1 - sin(x)^2
sin(x) = t
2 * (1 - t^2) + (2 - sqrt(2)) * t + sqrt(2) - 2 = 0
2 - 2*t^2 + 2t - sqrt(2)*t + sqrt(2) - 2 = 0
-2*t^2 + t*(2 - sqrt(2)) + sqrt(2) = 0
2*t^2 - t*(2 - sqrt(2)) - sqrt(2) = 0
t1,2 = (sqrt(2) - 2 +- sqrt(6 - 4sqrt(2) + 8sqrt(2)))/4
t1,2 = (sqrt(2) - 2 +- sqrt(6 + 4sqrt(2))/4
sqrt(6 + 4sqrt(2)) = 2 + sqrt(2)
t1,2 = (sqrt(2) - 2 +- (2 + sqrt(2)))/4
t1 = 2sqrt(2)/4 = sqrt(2)/2
t2 = -1
sin(x) = -1
x = 3p/2 + 2*pi*k
sin(x) = sqrt(2)/2
x = pi/4 + 2*pi*k
x = 5*pi/4 + 2*pi*k
Ответ:
x = 3p/2 + 2*pi*k
x = pi/4 + 2*pi*k
x = 5*pi/4 + 2*pi*k
k - любое целое