Answer
-$\frac{2}{\sqrt 3}$
Work Step by Step
Let's assume that reciprocal of -$\frac{\sqrt 3}{2}$ is '$ x$'.
By definition, product of a number and its reciprocal is always 1. Therefore-
$ (-\frac{\sqrt 3}{2})\times x $ = 1
$x$ = $\frac{1}{ (-\frac{\sqrt 3}{2})}$
or $ x$ = -$\frac{2}{\sqrt 3}$
i.e. reciprocal of -$\frac{\sqrt 3}{2}$ is -$\frac{2}{\sqrt 3}$
