Question

${lim}_{x\to 0}\frac{sin{x}^{\circ }}{x^{\circ }}$

Answer 1

${lim}_{x\to 0}\frac{sin{x}^{\circ }}{x^{\circ }}$

$={lim}_{x\to 0}\frac{sin\frac{x\times \pi }{180}}{x\times \frac{\pi }{180}}[\because 1^{\circ }=\frac{\pi }{180}radians]$

$={lim}_{\frac{\pi }{180}\to 0}\frac{sin\frac{\pi x}{180}}{\frac{\pi }{180}}[\because Ifx\to 0then\frac{\pi }{180}\to 0]$

$=1[\because {lim}_{x\to 0}\frac{sinx}{x}=1]$