Let $f$ and $g$ be real valued functions defined on interval $(-1,1)$ such that $g^{\prime \prime}(x)$ is continuous, $g(0) \neq 0, g^{\prime}(0)=0, g^{\prime \prime}(0) \neq$ 0 , and $f(x)=g(x) \sin x$.
STATEMENT -1 : $\lim _{x \rightarrow 0}[\mathrm{~g}(\mathrm{x}) \cot \mathrm{x}-\mathrm{g}(0) \operatorname{cosec} \mathrm{x}]=\mathrm{f}^{\prime \prime}(0)$.
and
STATEMENT -2 : $\mathrm{f}^{\prime}(0)=\mathrm{g}(0)$.