If x sin theta = y sin left( theta + frac{2pi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $x \sin 	heta = y \sin \left( 	heta + \frac{2\pi}{3} ight) = z \sin \left( 	heta + \frac{4\pi}{3} ight) = k$.Then $x = \frac{k}{\sin

Vedclass · Accepted Answer

$xy + yz + zx = 0$

Vedclass · Answer

(B) Let $x \sin 	heta = y \sin \left( 	heta + \frac{2\pi}{3} ight) = z \sin \left( 	heta + \frac{4\pi}{3} ight) = k$.Then $x = \frac{k}{\sin 	heta}$,$y = \frac{k}{\sin(	heta + 2\pi/3)}$,and $z = \frac{k}{\sin(	heta + 4\pi/3)}$.Consider the sum $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{k} [\sin 	heta + \sin(	heta + 2\pi/3) + \sin(	heta + 4\pi/3)]$.Using the identity $\sin A + \sin(A + 120^\circ) + \sin(A + 240^\circ) = 0$,we get $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$.This simplifies to $\frac{yz + zx + xy}{xyz} = 0$,which implies $xy + yz + zx = 0$.

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

Similar Questions

If $\sin (\alpha+\beta)=5 \sin (\alpha-\beta)$,then $\frac{\sin 2 \beta}{5-\cos 2 \beta}=$

If $\cosh 2x = 241$,then $\operatorname{coth} x$ is equal to

If $\pi < \alpha < \frac{3\pi}{2}$,then $\sqrt{\frac{1 - \cos \alpha}{1 + \cos \alpha}} + \sqrt{\frac{1 + \cos \alpha}{1 - \cos \alpha}} = $

$\sin ^2 5^{\circ}+\sin ^2 10^{\circ}+\sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ}$ is equal to

The value of the expression $\frac{2(\sin 1^{\circ} + \sin 2^{\circ} + \sin 3^{\circ} + \dots + \sin 89^{\circ})}{2(\cos 1^{\circ} + \cos 2^{\circ} + \dots + \cos 44^{\circ}) + 1}$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module