જો frac{x}{cos theta} = frac{y}{cos left( the | vedclass

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(B) ધારો કે $\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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$0$

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(B) ધારો કે $\frac{x}{\cos 	heta} = \frac{y}{\cos \left( 	heta - \frac{2\pi}{3} ight)} = \frac{z}{\cos \left( 	heta + \frac{2\pi}{3} ight)} = k.$તેથી,$x = k \cos 	heta, y = k \cos \left( 	heta - \frac{2\pi}{3} ight),$ અને $z = k \cos \left( 	heta + \frac{2\pi}{3} ight).$હવે,$x + y + z = k \left[ \cos 	heta + \cos \left( 	heta - \frac{2\pi}{3} ight) + \cos \left( 	heta + \frac{2\pi}{3} ight) ight].$સૂત્ર $\cos(A - B) + \cos(A + B) = 2 \cos A \cos B$ નો ઉપયોગ કરતા,$x + y + z = k \left[ \cos 	heta + 2 \cos 	heta \cos \left( \frac{2\pi}{3} ight) ight].$કારણ કે $\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.$તેથી,$x + y + z = 0.$

જો $\frac{x}{\cos \theta} = \frac{y}{\cos \left( \theta - \frac{2\pi}{3} \right)} = \frac{z}{\cos \left( \theta + \frac{2\pi}{3} \right)},$ હોય,તો $x + y + z = $

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જો $\sin \theta = \frac{1}{2} \left( \sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} \right)$,જ્યાં $x, y \in R - \{0\}$ હોય,તો:

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