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$\lim _{x \rightarrow \pi / 2}(\sec \theta-\tan \theta)=$
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$0$
$\lim _{\theta \rightarrow \pi / 2} \frac{1-\sin \theta}{\cos \theta}=\lim _{\theta \rightarrow \pi / 2} \frac{\left(\cos \frac{\theta}{2}-\sin \frac{\theta}{2}\right)^2}{\left(\cos \frac{\theta}{2}-\sin \frac{\theta}{2}\right)\left(\cos \frac{\theta}{2}+\sin \frac{\theta}{2}\right)}=0$.
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