Let $f(x)=\sin x, g(x)=x^2$ and $h(x)=\log _e x$. If F(x) = (hog of)(x), then F''(x) is equal to

$2 ~cosec^3 x$ $2 \cot x^2-4 x^2 ~cosec^2 x^2$ $2 x \cot x^2$ $-2 ~cosec^2 x$

$-2 ~cosec^2 x$

We have, F(x) = (hogof)(x) $\Rightarrow F(x) = h \{g(f(x)\}=h\{g(\sin x)\}=h\left(\sin ^2 x\right)$ $\Rightarrow F(x)=\log _e \sin ^2 x=2 \log _e \sin x$ $F'(x)=2 \cot x$  and  $f''(x)=-2 ~cosec^2 x$