Square root of a fraction

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I have the following variable and function:

var('r')
f = function('f')(r)

with an equation given by:

eq = sqrt(-1/(f^2*sin(r)^2))-1/sqrt(-f^2*sin(r)^2)

which, in LaTeX expression, looks like:

$$\begin{equation} \sqrt{-\frac{1}{f\left(r\right)^{2} \sin\left(r\right)^{2}}} - \frac{1}{\sqrt{-f\left(r\right)^{2} \sin\left(r\right)^{2}}} \end{equation}$$

In principle, this should be equal to zero. However,

bool(eq==0)

gives me False. I have tried with .simplify_full() and following the suggestion in here, I have used ._sympy_().simplify():

eq = eq._sympy_().simplify()
bool(eq==0)

but I still get False. Am I missing something?