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

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

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

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

If x/(costheta)=y/(cos(theta-(2pi)/3))=z/(cos(theta+(2pi)/3)) then x+y+z is

If x sintheta=ysin(theta+(2pi)/(3))=z sin(theta+(4pi)/(3)), then

If x,y,z are non zero real numbers and if x cos theta=y cos (theta+(2pi)/3)=z cos (theta+(4pi)/3) for some theta in R then show that xy+yz+zx=0

If xcostheta=ycos(theta+(2pi)/3)=zcos(theta+(4pi)/3) then the value of 1/x+1/y+1/z is equal to

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