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** Step-by-step Solution **

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Simplifying

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$\lim_{x\to\frac{\pi}{2}}\left(\frac{\cos\left(x\right)}{1-\sin\left(x\right)}\right)$

Learn how to solve problems step by step online. Find the limit (x)->(pi/2)lim(cos(x)/(1-sin(x))). Simplifying. If we directly evaluate the limit \lim_{x\to \frac{\pi}{2}}\left(\frac{\cos\left(x\right)}{1-\sin\left(x\right)}\right) as x tends to \frac{\pi}{2}, we can see that it gives us an indeterminate form. We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in.

** Final Answer

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