Limits, Continuity & Differentiability
Trigonometric Limits
Grade 12
Question:
<p>Find the value of \(\lim_{x \to \frac{\pi}{2}} \frac{\cos x}{\left(1 - \tan \frac{x}{2}\right)(1 - \sin x)}\left(1 + \tan \frac{x}{2}\right)(\pi - 2x)\)</p>
<p>(a) \(-\frac{1}{4}\)</p>
<p>(b) \(-\frac{1}{2}\)</p>
<p>(c) \(0\)</p>
<p>(d) \(\frac{1}{4}\)</p>
Step-by-Step Solution
Key Concept: Use trigonometric identities for \(\tan \frac{x}{2}\) and substitution to convert to a standard limit form
<p>Apply trigonometric identities and use substitution \(u = \pi - 2x\) as \(x \to \frac{\pi}{2}\).</p>
Correct Answer: B