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