lim _{x rightarrow pi / 2}(sec x-tan x) is eq | vedclass

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(D) $\lim _{x ightarrow \frac{\pi}{2}}(\sec x-	an x)$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \left(\frac{1-\sin x}{\cos x}ight)$ (wh

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(D) $\lim _{x ightarrow \frac{\pi}{2}}(\sec x-	an x)$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \left(\frac{1-\sin x}{\cos x}ight)$ (which is of the $\frac{0}{0}$ form)Applying $L$'$H$ôpital's rule by differentiating the numerator and denominator with respect to $x$:$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \frac{\frac{d}{dx}(1-\sin x)}{\frac{d}{dx}(\cos x)}$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \frac{-\cos x}{-\sin x}$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \cot x$Substituting $x = \frac{\pi}{2}$:$\Rightarrow \cot \frac{\pi}{2} = 0$

$\lim _{x \rightarrow \pi / 2}(\sec x-\tan x)$ is equal to

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