2sin(п/4+x)sin(п/4-x)+sin^2x=0

Решим уравнение 2 * sin (pi/4 + x) * sin (pi/4 - x) + sin^2 x = 0. 

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

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

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

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

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

cos^2 x - sin^2 x + sin^2 x = 0; 

cos^2 x + sin^2 x * (1 - 1) = 0; 

cos^2 x = 0; 

cos x = 0; 

x = pi/2 + pi * n, где n принадлежит Z.