lim_(x→(π/(20))) ((1−tan 5x)/(sin 5x−cos 5x)) ?


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Question Number 111907 by bemath last updated on 05/Sep/20

$\lim_{x \to \frac{π}{20}} \frac{1 - \tan 5 x}{\sin 5 x - \cos 5 x} ?$
	Answered by john santu last updated on 05/Sep/20

	Answered by john santu last updated on 05/Sep/20

	$a n o t h e r w a y$ $\lim_{x \to \frac{π}{20}} \frac{\cos 5 x - \sin 5 x}{\sin 5 x - \cos 5 x} . \frac{1}{\cos 5 x}$ $= - \lim_{x \to \frac{π}{20}} \frac{1}{\cos 5 x} = - \frac{1}{\cos (\frac{π}{4})} = - \sqrt{2}$
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