Question

If $2\cos x<\sqrt{3}$ and $xϵ[-\pi ,\pi ]$, then the solution set for $x$ is

• A. $[-\pi ,-\frac{\pi }{6})\cup (\frac{\pi }{6},\pi ]$
• B. $[-\frac{\pi }{6}\frac{\pi }{6}]$
• C. $[-\pi ,-\frac{\pi }{6}]\cup [\frac{\pi }{6},\pi ]$
• D. none of these

Answer 1

The correct option is A $[-\pi ,-\frac{\pi }{6})\cup (\frac{\pi }{6},\pi ]$

Given,

$2cosx<\sqrt{3}\Rightarrow cosx<\frac{\sqrt{3}}{2}$
we also know that $-1\le cosx\le 1$
considering both,
$-1\le cosx<\frac{\sqrt{3}}{2}$
Hence solution of $x$ in the given interval is,
$xϵ[-\pi ,\frac{-\pi }{6})\cup (\frac{\pi }{6},\pi ]$