If x, sin theta = y, sin , left( {theta ,, + | vedclass

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Question

$\frac{x}{y}\,\, = \,\frac{{\sin 2\pi /3\,.\,\,\cos 	heta \,\, + \,\cos 2\pi /3\,.\sin 	heta }}{{\sin 	heta }}$ 

$=$ $\frac{1}{2}\,\le

Vedclass · Accepted Answer

$xy + yz + zx = 0$

Vedclass · Answer

$\frac{x}{y}\,\, = \,\frac{{\sin 2\pi /3\,.\,\,\cos 	heta \,\, + \,\cos 2\pi /3\,.\sin 	heta }}{{\sin 	heta }}$ 

$=$ $\frac{1}{2}\,\left[ {\frac{{\sqrt 3 \,\cos 	heta \, - \,\sin 	heta }}{{\sin 	heta }}} ight]$

$=$$\frac{{\sqrt 3 }}{2}\,\cot 	heta \, - \,\frac{1}{2}$ ....$(1)$

$|||^{1y}$   $\frac{x}{z}\,\, = \,\,\frac{{\sin 	heta \,.\,\cos 4\pi /3\,\, + \,\,\cos 	heta \,.\,\sin 4\pi /3}}{{\sin 	heta }}$ 

$=$ $ - \,\,\frac{1}{2}\,\, - \,\,\frac{{\sqrt 3 }}{2}\,\,\cot 	heta $ ....$(2)$

$\frac{x}{y}\,\, + \,\,\frac{x}{z}\,\, = \,\, - 1$

$\Rightarrow xz + xy + yz = 0$

If $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ then :

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