Question

The least positive solution of $cot(\frac{\pi}{3\sqrt{3}} sin \,2x) = \sqrt{3}$ lies in

• A. $(0, \frac{\pi}{6}]$
• B. $(\frac{\pi}{9}, \frac{\pi}{6})$
• C. $(\frac{\pi}{12}, \frac{\pi}{9}]$
• D. $(\frac{\pi}{3}, \frac{\pi}{2}]$

Answer 1

Answer: (A)

$cot (\frac{\pi}{3\sqrt{3}} sin\,2x) = \sqrt{3}$
$\Rightarrow \frac{\pi}{3\sqrt{3}} sin\,2x = n\pi + \frac{\pi}{6}, n \in Z$
$\Rightarrow sin\,2x = 3\sqrt{3} \,n + \frac{\sqrt{3}}{2}$
For least positive solution, $n = 0$
$\Rightarrow sin\,2x = \frac{\sqrt{3}}{2}$
$\Rightarrow 2x = \frac{\pi}{3}$
$\Rightarrow x = \frac{\pi}{6}$