lim_(x→0) ((1/(sin^2 x))−(1/x^2 ))=? please solve it describely.


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Question Number 170166 by sciencestudent last updated on 17/May/22

$l i \underset{x \to 0}{m} (\frac{1}{{s i n}^{2} x} - \frac{1}{x^{2}}) = ?$ $p l e a s e s o l v e i t d e s c r i b e l y .$
Commented by mr W last updated on 17/May/22

$i t i s s o l v e d d e s c r i p t i v e l y e n o u g h!$ $i f y o u {d o n}^{'} t u n d e r s t a n d s o m e t h i n g,$ $y o u c a n t e l l w h a t y o u {d o n}^{'} t$ $u n d e r s t a n d, i n s t e a d o f p o s t i n g t h e$ $s a m e q u e s t i o n a g a i n a n d a g a i n .$
	Answered by ajfour last updated on 17/May/22

	$c o n s i d e r \lim_{x \to 0} a p l p i e d o n$ $b o t h s i d e s o f s t e p s t h a t f o l l o w$ $({L x}^{2} + 1) = {(\frac{x}{\sin x})}^{2}$ $2 L x = 2 (\frac{x}{\sin x}) (\frac{\sin x - x \cos x}{\sin^{2} x})$ $L = \frac{\sin x - x \cos x}{\sin^{3} x}$ $= \frac{\cos x - (\cos x - x \sin x)}{3 \sin^{2} x}$ $= \frac{1}{3} (\frac{x}{\sin x}) = \frac{1}{3}$
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