\( \lim _{x \rightarrow 0} \frac{x^{a} \sin ^{b} x}{\sin \left(x^{c}\right)} \), where \( a, b, ...

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\( \lim _{x \rightarrow 0} \frac{x^{a} \sin ^{b} x}{\sin \left(x^{c}\right)} \), where \( a, b, c \in R \sim\{0\} \), exists and has non-zero value. Then,
(A) \( a+c=b \)
(B) \( b+c=a \)
(C) \( a+b=c \)
(D) None of these
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