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I have a function like this:

$$f(x) = \Big(1-\frac{1}{\cos x}\Big)\frac{1}{\sin x}$$

I need to evaluate the limit of this function when $x\rightarrow \pi /2$. A simple calculation shows that the function blows to infinity. Is there any way to get a finite limit out of this function?

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  • $\begingroup$ What do you mean? $\endgroup$
    – Robert Z
    Jan 22, 2019 at 13:25
  • $\begingroup$ I mean to ask is there any technique (or some mathematical manipulation) through which we can get a finite value of f(x) when x approaches pi/2. $\endgroup$
    – Scholar
    Jan 22, 2019 at 13:27
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    $\begingroup$ The limit is unique. If it is infinite it remains infinite. $\endgroup$
    – Robert Z
    Jan 22, 2019 at 13:28
  • $\begingroup$ @Robert: Oh..okay. $\endgroup$
    – Scholar
    Jan 22, 2019 at 13:30

1 Answer 1

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Write $$\frac{\cos(x)-1}{\cos(x)}\cdot \frac{1}{\sin(x)}\cdot \frac{\cos(x)+1}{\cos(x)+1}$$

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  • $\begingroup$ The limit is still infinite. $\endgroup$
    – Scholar
    Jan 23, 2019 at 17:14

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