Let \( f \) and \( g \) be real valued functions defined on \( \mat...

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Let \( f \) and \( g \) be real valued functions defined on
\( \mathrm{P} \) interval \( (-1,1) \) such \( g^{\prime \prime}(x) \) is continuous, \( g(0) \neq 0 \).

W \( g^{\prime}(0)=0, g^{\prime \prime}(0) \neq 0 \), and \( f(x)=g(x) \sin x \)
STATEMENT-1:
\( \lim _{x \rightarrow 0}[g(x) \cot x-g(0) \operatorname{cosec} x]=f^{\prime \prime}(0) \) and
STATEMENT-1: \( f^{\prime}(0)=g(0) \)
(A) Statement-1 is True, statement-2 is True:
Statement-2 is a correct explanation for
Statement-1
(B) Statement-1 is True, statement-2 is True:
Statement-2 is NOT a correct explanation for
Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
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