" If "x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3))," prove that "xy+yz+zx=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 x costheta=y cos (theta+(2pi)/3)=z cos(theta+(4pi)/3) show that xy + yz+ zx = 0

If x*cos theta=y*cos(theta+(2 pi)/(3))=2*cos(theta+(4 pi)/(3)) then evaluate xy+yz+zx

If xsintheta=ysin(theta+(2pi)/3)=z sin (theta+(4pi)/3), ,prove that xy + yz + zx = 0.

If x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3)), then write the value of (1)/(x)+(1)/(y)=(1)/(z)

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

If x cos theta = y cos (theta + (2pi)/(3)) = z cos (theta + (4pi)/(3)) , find the value of xy + yz + zx