If `x cos alpha = y cos ( 2pi//3+ alpha ) = z cos ( 4pi//3+ alpha ) , " then " xy+yz+zx=`

(cos alpha + (cos ((2 pi) / (3) + alpha)) + cos ((4 pi) / (3) + alpha))

Eliminating alpha from xcos alpha = y cos(alpha +2pi/3) = zcos (alpha +4pi/3) establish that xy + yz + zx= 0

I : If x cos theta = y cos (120^@ + theta ) = z cos ( theta + 240^(@)) then xy+ yz+ zx=1 II : cos alpha + cos (120^(@) + alpha ) + cos (120^@ - alpha ) =0

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

If cos (2pi)/3 =sin alpha ,which could be alpha ?

Find the sum to n terms of the following series: cos alpha + cos (pi - alpha) + cos (2pi + alpha) + .......(0 < alpha < (pi)/2) .