If$\ \ \frac{x}{\cos heta} = \frac{y}{\cos\left( heta - \frac{2\pi}{3} ight)} = \frac{\mathcal{z}}{\cos\left( heta + \frac{2\pi}{3} ight)},\ then\ x + y + \mathcal{z\ }$is equal to

Question

If$\ \ \frac{x}{\cos	heta} = \frac{y}{\cos\left( 	heta - \frac{2\pi}{3} ight)} = \frac{\mathcal{z}}{\cos\left( 	heta + \frac{2\pi}{3} ight)},\ then\ x + y + \mathcal{z\ }$is equal to

Dr. Abubacker · Accepted Answer

(b)
We have,$\ \ \frac{x}{\cos	heta} = \frac{y}{\cos\left( 	heta - \frac{2\pi}{3} ight)} = \frac{\mathcal{z}}{\cos\left( 	heta + \frac{2\pi}{3} ight)}$
Therefore, each ratio is equal to$\ \ \frac{x + y + \mathcal{z}}{\cos{	heta + \cos{\left( 	heta - \frac{2\pi}{3} ight) + \cos\left( 	heta + \frac{2\pi}{3} ight)}}}$
$= \frac{x + y + \mathcal{z}}{\cos{	heta + 2\cos{	heta\cos\frac{2\pi}{3}}}}$
$= \frac{x + y + \mathcal{z}}{0}$
$\Rightarrow x + y + \mathcal{z} = 0$

Q. If$\ \ \frac{x}{\cos\theta} = \frac{y}{\cos\left( \theta - \frac{2\pi}{3} \right)} = \frac{\mathcal{z}}{\cos\left( \theta + \frac{2\pi}{3} \right)},\ then\ x + y + \mathcal{z\ }$is equal to

Explanation

Reviewed by Dr. Abubacker

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