Answer:
Option B
Explanation:
g(x)=\int_{x}^{\frac{\pi}{2}} f'(t) cosec t f(t)-\cot t cosec t f(t)] dt
g(x)= f(\frac{\pi}{2}) cosec \frac{\pi}{2}-f(x) cosec x
\Rightarrow g(x)=3-\frac{f(x)}{\sin x}
\lim_{x \rightarrow 0}g(x)=\lim_{x \rightarrow 0}(\frac{3\sin x-f(x)}{\sin x})
=\lim_{x \rightarrow 0}\frac{3\cos x-f'(x)}{\cos x}
\frac{3-1}{1}=2