Question

Evaluate:
$\rm \displaystyle \lim_{x\to 0}\ \frac{\sin (mx^{\circ})}{\sin (nx^{\circ})}$

Answer 1

Solution :

$\rm \displaystyle \lim_{x\to 0}\ \frac{\sin (mx^{\circ})}{\sin (nx^{\circ})}$

= $\rm \displaystyle \lim_{x\to 0}\ \frac{\frac{\sin (mx^{\circ})}{mx}}{\frac{\sin (nx^{\circ})}{nx}} \times \frac{mx}{nx}$

= $\rm \displaystyle \frac{m}{n}$

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