Question

Solve the equation.
cosec 3x = $\frac{-2}{\sqrt{3}}$

Answer 1

As

$cosec \: 3x = \frac{ - 2}{ \sqrt{3} } \\ \\ 3x = {cosec}^{ - 1} ( \frac{ - 2}{ \sqrt{3} } ) \\ \\ 3x = {cosec}^{ - 1} (cosec( - \frac{\pi}{3} ) \\ \: \: because - \frac{\pi}{3} \: belongs \: to \: principal \: value \: branch \: of \: {cosec}^{ - 1} \\ \\ 3x = \frac{ - \pi}{3} \\ \\ x = \frac{ - \pi}{9}$