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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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If $\large\frac{x}{\cos\theta}=\frac{y}{\cos(\theta+\large\frac{2\pi}{3})}=\frac{z}{\cos(\theta-\large\frac{2\pi}{3})}$ then $x+y+z$ is equal to

$(a)\;-1\qquad(b)\;1\qquad(c)\;0\qquad(d)\;None\;of\;these$

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1 Answer

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Given :
$\large\frac{x}{\cos\theta}=\frac{y}{\cos(\theta+\large\frac{2\pi}{3})}=\frac{z}{\cos(\theta-\large\frac{2\pi}{3})}$
Let the given equation be equal to $\lambda$
$\Rightarrow x+y+z=\lambda\{\cos\theta+\cos(\theta+\large\frac{2\pi}{3})$$+\cos(\theta-\large\frac{2\pi}{3})\}$
$\Rightarrow x+y+z=\lambda[\cos\theta+2\cos\theta\cos\large\frac{2\pi}{3}]$
$\Rightarrow x+y+z=0$
Hence (c) is the correct answer.
answered Oct 10, 2013 by sreemathi.v
 

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