If `asinx`=`bsin(x+(2pi)/3)=csin(x+(4pi)/3)`, prove that ab+bc+ca=0

If a sin theta=bsin(theta+(2 pi)/(3))=csin(theta+(2 pi)/(3)) prove that ab+bc+ca=0

If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(4pi)/3) , prove that a b+b c+c a=0.

If asintheta=bsin(theta+(2pi)/(3))=csin(theta+(4pi)/(3)) then prove that, ab+bc+ca=0 .

If a cos theta = b cos ( theta+(2 pi)/3)= c cos ( theta+ (4pi)/3),"prove that" ab+bc+ca=0.

If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y+y z+z x=0.

If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y+y z+z x=0.

If asintheta = bsin(theta+(2pi)/(3)) = csin(theta+(4pi)/(3)) , then the value of ab+bc+ca is ___________.

If a= b cos ""(2pi)/(3) = c cos ""(4pi)/(3), then the value of (ab+ bc +ca) is-

If a=b(cos(2 pi))/(3)=(cos(4 pi))/(3), then write the value o ab+bc+ca