यदि frac{x}{cos theta} = frac{y}{cos left( th | vedclass

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(B) माना कि $\frac{x}{\cos 	heta} = \frac{y}{\cos \left( 	heta - \frac{2\pi}{3} ight)} = \frac{z}{\cos \left( 	heta + \frac{2\pi}{3} ight)} = k

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(B) माना कि $\frac{x}{\cos 	heta} = \frac{y}{\cos \left( 	heta - \frac{2\pi}{3} ight)} = \frac{z}{\cos \left( 	heta + \frac{2\pi}{3} ight)} = k.$अतः,$x = k \cos 	heta, y = k \cos \left( 	heta - \frac{2\pi}{3} ight),$ और $z = k \cos \left( 	heta + \frac{2\pi}{3} ight).$अब,$x + y + z = k \left[ \cos 	heta + \cos \left( 	heta - \frac{2\pi}{3} ight) + \cos \left( 	heta + \frac{2\pi}{3} ight) ight].$सूत्र $\cos(A - B) + \cos(A + B) = 2 \cos A \cos B$ का उपयोग करने पर,$x + y + z = k \left[ \cos 	heta + 2 \cos 	heta \cos \left( \frac{2\pi}{3} ight) ight].$चूंकि $\cos \left( \frac{2\pi}{3} ight) = -\frac{1}{2},$$x + y + z = k \left[ \cos 	heta + 2 \cos 	heta \left( -\frac{1}{2} ight) ight] = k [\cos 	heta - \cos 	heta] = k(0) = 0.$अतः,$x + y + z = 0.$

यदि $\frac{x}{\cos \theta} = \frac{y}{\cos \left( \theta - \frac{2\pi}{3} \right)} = \frac{z}{\cos \left( \theta + \frac{2\pi}{3} \right)},$ है,तो $x + y + z = $

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