Answer:
Option D
Explanation:
$\lim_{x \rightarrow 0}\frac{\sin(\pi\cos^{2}x)}{x^{2}}$
= $\lim_{x \rightarrow 0}\frac{\sin\pi(1-\sin^{2}x)}{x^{2}}$
= $\lim_{x \rightarrow 0}\frac{\sin(\pi-\pi\sin^{2}x)}{x^{2}}$
=$\lim_{x \rightarrow 0}\frac{\sin(\pi\sin^{2}x)}{x^{2}}$
[ $\because$ $\sin(\pi-\theta)=\sin\theta$ ]
$=\lim_{x \rightarrow0}\frac{\sin\pi\sin ^{2}x}{\pi\sin^{2}x}\times (\pi)\left[\frac{\sin^{2}x}{x^{2}}\right]$
= $\pi$ [$\lim_{x \rightarrow0}\frac{\sin\theta}{\theta}=1$]
