Question

Evaluate the limit \( \lim_{\theta \to \frac{\pi}{2}} \frac{1 - \sin \theta}{\left(\frac{\pi}{2} - \theta\right)\cos \theta} \)

• A. \( -\frac{1}{2} \)
• B. \( -1 \)
• C. 1
• D. \( \frac{1}{2} \)

Hint:

To resolve indeterminate forms such as \( \frac{0}{0} \) in limits, L'Hopital's Rule is a powerful method, which involves differentiating the numerator and denominator separately and then evaluating the limit.

Answer 1

The Correct Option is D