Nilai \( \displaystyle \lim_{\theta \to 0} \ \frac{1-\cos m\theta}{1-\cos n\theta} = \cdots \)
Pembahasan:
\begin{aligned} \lim_{\theta \to 0} \ \frac{1-\cos m\theta}{1-\cos n\theta} &= \lim_{\theta \to 0} \ \frac{2 \sin^2 \frac{1}{2} m\theta}{2 \sin^2 \frac{1}{2} n\theta} \\[8pt] &= \lim_{\theta \to 0} \ \frac{ \displaystyle \frac{\sin^2 \frac{1}{2} m\theta}{\theta^2} }{ \displaystyle \frac{\sin^2 \frac{1}{2} n\theta}{\theta^2} } \\[8pt] &= \frac{\frac{1}{2}m \cdot \frac{1}{2}m}{ \frac{1}{2}n \cdot \frac{1}{2}n } \\[8pt] &= \frac{m^2}{n^2} \end{aligned}