x= y cos 2pi/3 = z cos 4 pi/3 ,then xy+yz+zx=

Your answer is 0. Knowing that x = y cos 2pi/3 = z cos 4pi/3, we can come to a relation between each x and y and x and z. the values for both cos 2pi/3 and 4pi/3 is -0.5. so we can calculate that y = -2x = z... Solving the given equation becomes quite easy then. The key to this question is to keep your eyes open for values of cos 2pi/3 and cos 4pi/3.