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What is value of

If x=ycos(2∏/3)=zcos(4∏/3) , Then xy+yz+zx is equal to ?

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both is the cosine of 2pi/3 and 4pi/3 = -0.5. since pi/3 = 60 degrees, 2pi/3 is 120 and 4pi/3 is 240, putting them in the 2nd and 3rd quadrant, where cosine is negative
You can then set up that x = -.5y = -.5z
xy = -.5y*y (substituting -.5y for x) and from the above equation y = z so yz = y2
since y = z, then xz is the same as xy.  Add them up and you will see the answer.
Dorene O.