1) sinx (1-cosx) ^2+cosx (1-sinx) ^2=2 2) сosx=sin2x*cosx

Решим уравнения:

1) sin x * (1 - cos x) ^2 + cos x * (1 - sin x) ^2 = 2;

sin x * (1 - 2 * cos x + cos^2 x) + cos x * (1 - 2 * sin x + sin^2 x) = 2;

sin x - 2 * cos x * sin x + cos^2 x * sin x + cos x - 2 * sin x * cos x + sin^2 x * cos x = 2;

sin x - 2 * cos x * sin x + cos^2 x * sin x + cos x - 2 * sin x * cos x + sin^2 x * cos x - 2 = 0;

(sin x + cos x) - 4 * cos x * sin x + sin x * cos x * (cos x + sin x) - 2 * sin^2 x - 2 * cos^2 x = 0;

(sin x + cos x) + sin x * cos x * (cos x + sin x) - 2 * (sin^2 x + 2 * sin x * cos x + cos^2 x) = 0;

(sin x + cos x) + sin x * cos x * (cos x + sin x) - 2 * (sin x + cos x) ^2 = 0;

(sin x + cos x) * (1 + sin x * cos x - 2 * (sin x + cos x)) = 0;

(sinx + cos x) = 0;

sin (2 * x) = - 1;

2 * x = pi/2 + 2 * pi * n;

x = pi/4 + pi * n.

2) сos x = sin (2 * x) * cos x;

сos x - sin (2 * x) * cos x = 0;

cos x * (1 - sin (2 * x)) = 0;

{ cos x = 0;

1 - sin (2 * x) = 0;

{ x = pi/2 + pi * n;

sin (2 * x) = 1;

{ x = pi/2 + pi * n;

2 * x = pi/2 + 2 * pi * n;

{ x = pi/2 + pi * n;

x = pi/2/2 + 2 * pi * n/2;

{ x = pi/2 + pi * n;

x = pi/4 + pi * n, где n принадлежит Z.