Sinx+cosx*ctgx/2 = - корень из 3

Sinx+cosx*cos (x/2) / sin (x/2) = - √3

(sinx*sin (x/2) + cosx*cos (x/2)) = - √3sin (x/2)

sin (x/2) ≠0⇒x/2≠πn⇒x≠2πn

cos (x-x/2) = - √3sin (x/2)

cos (x/2) + √3sin (x/2) = 0

2 (1/2*cos (x/2) + √3/2*sin (x/2)) = 0

2sin (π/6 + (x/2)) = 0

π/6 + (x/2) = πn

x/2=-π/6+πn

x=-π/3+2πn