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$\lim\limits_{\theta \to \Large\frac{\pi}{2}}(\sec\theta-\tan\theta)$=

$(a)\;0\qquad(b)\;1\qquad(c)\;-1\qquad(d)\;2$

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Given limit=$\lim\limits_{\large\theta\to\large\frac{\pi}{2}}\big(\large\frac{1}{\cos\theta}-\frac{\sin\theta}{\cos\theta}\big)$
$\Rightarrow \lim\limits_{\theta\to \large\frac{\pi}{2}}\large\frac{1-\sin\theta}{\cos\theta}\big(\large\frac{0}{0}\big)$
$\Rightarrow\lim\limits_{\theta\to \large\frac{\pi}{2}}\large\frac{-\cos\theta}{-\sin\theta}$
$\Rightarrow \large\frac{0}{1}$
$\Rightarrow 0$
Hence (a) is the correct answer.
answered Dec 24, 2013 by sreemathi.v
 

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