Sinx+cosx*ctgx/2 = - корень из 3

Question

Sinx+cosx*ctgx/2 = - корень из 3

Answer 1

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