1+ctg2x=1\cos(3п\2-2x)

Решим уравнение 1 + ctg (2 * x) = 1/cos(3 * pi/2 - 2 * x). 

1 + ctg (2 * x) = 1/cos(3 * pi/2 - 2 * x); 

1 + ctg (2 * x) = 1/(-sin (2 * x)); 

1 + ctg (2 * x) = - 1/(sin (2 * x));  

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

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

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

sin (2 * x) + cos (2 * x) = -1; 

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

sin (2 * x) + 2 * cos^2 x = 0; 

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

sin^2 x - sin x * cos x - 1 = 0;  

1 - cos^2 x - sin x * cos x - 1 = 0; 

cos^2 x + sin x * cos x = 0; 

cos x * (cos x + sin x) = 0; 

1) cos x = 0; 

x = pi/2 + pi * n; 

2) cos x + sin x = 0; 

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

sin (2 * x) = -1; 

2 * x = -pi/2 + 2 * pi * n; 

x = -pi/4 + pi * n.