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Let \( f \) be a function defined on \( (-1,1) \)
\[
f(x)=\frac{\cos ^{-1}\left(1-\{x\}^{2}\right) \sin ^{-1}(1-\langle x))}{\{x\}-\{x\}^{3}}, x \neq 0 \text { and (|) }
\]
is the fractional part function.
(A) \( \lim _{x \rightarrow 0^{+}} f(x) \) exists and equals \( \frac{\pi}{\sqrt{2}} \)
(B) \( \lim _{x \rightarrow 0^{-}} f(x) \) exists and equals \( \frac{\pi}{2} \)
(C) \( \lim _{x \rightarrow 0^{+}} f(x) \) exists and equals \( \frac{\pi}{4} \)
(D) \( \lim _{x \rightarrow 0^{-}} f(x) \) exists and equals \( \frac{\pi}{\sqrt{2}} \)
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