Question

Evaluate: $\underset{\theta \to \pi /2}{lim}(\sec \theta -\tan \theta ).$

Answer 1

$\underset{\theta \to \pi /2}{lim}(\sec \theta -\tan \theta )$ form $(\infty -\infty )$
$=\underset{\theta \to \pi /2}{lim}\frac{1-\sin \theta }{\cos \theta }\left(\frac{0}{0}\right)$
So using L-Hospital's rule,
$=\underset{\theta \to \pi /2}{lim}\frac{-\cos \theta }{-\sin \theta }=0$