limlimits_x → 0≤ft((sin ≤ft(π cos ^2 x))/(x^2)) equals

$\lim\limits_{x \rightarrow 0} \frac{\sin (\pi(1-(\sin x)^2))}{x^2}$

$=\lim\limits_{x \rightarrow 0} \frac{\pi \sin \pi \sin ^2 x}{\pi \sin ^2 x} . \frac{\sin ^2 x}{x^2}$

$=\pi$

Hence (2) is the correct answer.