Lim-pi/2 (sec x - tan x)

\lim_{x \to \frac{π}{2}} (\sec x - \tan x) = \lim_{x \to \frac{π}{2}} [\frac{1}{\cos x} - \frac{\sin x}{\cos x}] = \lim_{x \to \frac{π}{2}} (\frac{1 - \sin x}{\cos x}) = \lim_{x \to \frac{π}{2}} [\frac{1 - \cos (π / 2 - x)}{\sin (π / 2 - x)}] = \lim_{x \to \frac{π}{2}} \frac{2 \sin^{2} (\frac{π}{4} - \frac{x}{2})}{2 \sin (\frac{π}{4} - \frac{x}{2}) \cos (\frac{π}{4} - \frac{x}{2})} = \lim_{x \to \frac{π}{2}} \frac{\sin (\frac{π}{4} - \frac{x}{2})}{\cos (\frac{π}{4} - \frac{x}{2})} = \lim_{x \to \frac{π}{2}} [\tan (\frac{π}{4} - \frac{x}{2})] = \tan (\frac{π}{4} - \frac{π}{4}) = \tan 0 = 0

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