Let f(x)=sin πcos2 xx2,x≠0 The value of f(0) so that f is a continuous function is

limx→0 sin π1-sin2 xx2=limx→0 sin πsin2 xπsin2 x⋅πsin2 xx2=π

limx→0 sin π1-sin2 xx2=limx→0 sin πsin2 xπsin2 x⋅πsin2 xx2=π

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Let $f (x) = \frac{\sin (π \cos^{2} x)}{x^{2}}, x \neq 0$ The value of $f (0)$ so that f is a continuous function is

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$- π$

$π$

$\frac{π}{2}$

answer is B.

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$\lim_{x \to 0} \frac{\sin π (1 - \sin^{2} x)}{x^{2}} = \lim_{x \to 0} \frac{\sin (π \sin^{2} x)}{π \sin^{2} x} \cdot \frac{π \sin^{2} x}{x^{2}} = π$

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