Question

If $\frac{x}{cos\theta }=\frac{y}{cos(\theta -\frac{2\pi }{3})}=\frac{z}{cos(\theta +\frac{2\pi }{3})},$ then x + y + z=

• A. 1
• B. \N
• C. -1
• D. None of these

Answer 1

The correct option is B \N

We have $\frac{x}{cos\theta }=\frac{y}{cos(\theta -\frac{2\pi }{3})}=\frac{z}{cos(\theta +\frac{2\pi }{3})}=k$
$\Rightarrow x=kcos\theta ,y=kcos(\theta -\frac{2\pi }{3}),z=kcos(\theta +\frac{2\pi }{3})$
$\Rightarrow x+y+z=k[cos\theta +cos(\theta -\frac{2\pi }{3})+cos(\theta +\frac{2\pi }{3})]$
$=k\left[\right(0)=0$
$\Rightarrow x+y+z=0.$