If x = y cos frac{2pi}{3} = z cos frac{4pi}{3 | vedclass

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(B) Given the equation $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$.We know that $\cos \frac{2\pi}{3} = \cos(120^\circ) = -\frac{1}{2}$ and $\c

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(B) Given the equation $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$.We know that $\cos \frac{2\pi}{3} = \cos(120^\circ) = -\frac{1}{2}$ and $\cos \frac{4\pi}{3} = \cos(240^\circ) = -\frac{1}{2}$.Substituting these values,we get $x = y(-\frac{1}{2}) = z(-\frac{1}{2})$.Let $x = y(-\frac{1}{2}) = z(-\frac{1}{2}) = k$,where $k$ is a constant.Then $x = k$,$y = -2k$,and $z = -2k$.Now,calculate the expression $xy + yz + zx$:$xy + yz + zx = (k)(-2k) + (-2k)(-2k) + (-2k)(k)$$= -2k^2 + 4k^2 - 2k^2$$= 0$.

If $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$,then $xy + yz + zx = $

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