Sinx*cos(x+pi/3)+cosx*sin(x+pi/3)=0

Question

Sinx*cos(x+pi/3)+cosx*sin(x+pi/3)=0

Answer 1

Sinx*cos(x+π/3)+cosx*sin(x+π/3)  =0 ;
* * * sinαcosβ +cosα*sinβ =sin(α+β) * * *
sin(x+x+π/3) =0 ;
sin(2x+π/3) =0 ;
2x+π/3 =πk , k∈Z.
2x= -π/3 +πk , k∈Z.
x= -π/6 +(π/2)*k , k∈Z.