Решите sin2x-√3*sinx-√2*cosx+√6/2=0

2sin x*cos x - sgrt3*sin x - sgrt2*cos x + sgrt3*sgrt2 / 2 = 0;

(2 sin x*cos x - sgrt2*cos x) - (sgrt3*sin x - sgrt3/sgrt2) = 0;

(sgrt2*sgrt2*cos x - sgrt2*cosx) - (sgrt3*sinx - sgrt3/sgrt2) = 0;

sgrt2*cosx (sgrt2*sinx - 1) - sgrt3 (sin x - 1/sgrt2) = 0;

sgrt2*cosx (sgrt2*sinx - 1) - sgrt3/sgrt2 (sgrt2*sin x - 1) = 0;

(sgrt2*sin x - 1) (sgrt2*cos x - sgrt3/sgrt2) = 0;

1) sgrt2*sinx - 1 = 0;

sin x = 1/sgrt2;

sin x = sgrt2/2;

x = (-1) ^k * pi/4 + pi*k; k-Z

2) sgrt2*cos x - sgrt3 / sgrt2 = 0;

cosx = sgrt3/2;

x = + - pi/3 + 2 pi*k; k-Z