is equal to

Engineering

Mathematics

Trigonometric Limits

Question

$\underset{x \to 0}{Lim} \frac{\sin ({πcos}^{2} x)}{x^{2}}$ is equal to

$\frac{π}{2}$

– π

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$\underset{x \to 0}{Lim} \frac{\sin (π (1 - \sin^{2} x))}{x^{2}}$

$= \underset{x \to 0}{Lim} (\frac{\sin ({πsin}^{2} x)}{π \sin^{2} x}) \frac{π \sin^{2} x}{x^{2}} = π$