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यदि $x\cos \theta = y\cos \,\left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \,\left( {\theta + \frac{{4\pi }}{3}} \right)$ , तब $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ बराबर है
$1$
$2$
$0$
$3\,\,\cos \theta $
Solution
(c) दिया है
$x\cos \theta = y\cos \left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \left( {\theta + \frac{{4\pi }}{3}} \right) = k$
==> $\cos \theta = \frac{k}{x},\cos \left( {\theta + \frac{{2\pi }}{3}} \right) = \frac{k}{y}$ व $\cos \left( {\theta + \frac{{4\pi }}{3}} \right) = \frac{k}{z}$
अत: $\frac{k}{x} + \frac{k}{y} + \frac{k}{z} = \cos \theta + \cos \left( {\theta + \frac{{2\pi }}{3}} \right) + \cos \left( {\theta + \frac{{4\pi }}{3}} \right)$
$ = \cos \theta + \cos \left( {\frac{\pi }{3} – \theta } \right) – \cos \left( {\frac{\pi }{3} + \theta } \right)$
$ = \cos \theta – 2\cos \frac{\pi }{3}\cos \theta = 0$.
