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

sqrt (3 /sqrt(2) cos x - 1) +sin x =0

sqrt (3 /sqrt(2) cos x - 1) = - sin x

3/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=0

1/(1+t^2) (-4t^2/(1+t^2)+3/sqrt(2) *(1-t^2))-1=0

1/(1+t^2) (-4t^2+3/sqrt(2) *(1-t^4))/(1+t^2)-1=0

1/(1+t^2)^2 * (-4t^2+ 3/sqrt(2)(1-t^4) - (1+t^2)^2) =0

1/(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 )=0

t^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*n

x=2*Pi-2*arctan (sqrt(sqrt(36+4 (3+sqrt(2))/sqrt(2)) -6)/ (2 *(3+sqrt(2))/sqrt(2)))+2*Pi*n