sqrt (3/sqrt 2) cosx-1)+sinx=0

sqrt (3 /sqrt (2) cos x — 1)+sin x=0sqrt (3 /sqrt (2) cos x — 1)=- sin x3/sqrt (2) cos x — 1=sin^2 x-sin ^2 x+3/sqrt (2) cos x -1=0 замена sin x=2t/ (1+t^2) cos x=(1-t^2) / (1+t^2) -4t^2/ (1+t^2) ^2+3/sqrt (2)*(1-t^2) / (1+t^2) — 1=01/ (1+t^2) (-4t^2/ (1+t^2)+3/sqrt (2)*(1-t^2) -1=01/ (1+t^2) (-4t^2+3/sqrt (2)*(1-t^4) / (1+t^2) -1=01/ (1+t^2) ^2*(-4t^2+3/sqrt (2) (1-t^4) — (1+t^2) ^2)=01/ (1+t^2) ^2*(- (3+sqrt (2) /sqrt (2) t^4 -6t^2-1)=0 (- (3+sqrt (2) /sqrt (2) t^4 -6t^2-1)=0t^2=z (- (3+sqrt (2) /sqrt (2) z^2 -6z-1)=0 D=36+4 (3+sqrt (2) /sqrt (2) z=- (6- sqrt (36+4 (3+sqrt (2) /sqrt (2) / (2*(3+sqrt (2) /sqrt (2) z=- (6+sqrt (36+4 (3+sqrt (2) /sqrt (2) / (2*(3+sqrt (2) /sqrt (2) <0 не входит в ОДЗ z=(sqrt (36+4 (3+sqrt (2) /sqrt (2) -6) / (2*(3+sqrt (2) /sqrt (2) t=sqrt (sqrt (36+4 (3+sqrt (2) /sqrt (2) -6) / (2*(3+sqrt (2) /sqrt (2) с учетом универсальной замены t=tg (x/2) x=2*arctan (sqrt (sqrt (36+4 (3+sqrt (2) /sqrt (2) -6) / (2*(3+sqrt (2) /sqrt (2)+2*Pi*nx=2*Pi-2*arctan (sqrt (sqrt (36+4 (3+sqrt (2) /sqrt (2) -6) / (2*(3+sqrt (2) /sqrt (2)+2*Pi*n